Logical Connectives (Part 2) - Logical Reasoning Video Lecture | UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making

hello and welcome to a due southeast
lecture on logical consistency now this
is a very confusing topic as we have a
lot of logical connectives which are a
little difficult to decipher what they
actually mean so make sure you pay too
much tension in this video lecture so
what is logical consistency a set of
claims which are logically possible now
the first thing we do in this lecture is
defining logical connectives in logical
connectives the basic constituents are
simple propositions or promises which
are combined into complex propositions
by means of some logical words like not
and or and if for example if it rains
the ground will get wet it glitters only
if it is cold either I like tea or
coffee so we'll take this logical
connectives like if only if either and
or one by one some of the useful tips
throughout this video presentation the
first thing you have to do is to
identify what is the cause and what is
the effect the second thing you have to
think in your mind is is the cause
sufficient condition for the effect that
is does the cause always result in the
effect or just sometimes the third
condition is is the cause a necessary
condition but not sufficient for the
effect to take place that is can the
effect also take place because of some
other cause or not as we proceed with
this video presentation all these three
things will be more clear let's take up
the first connective here which is if so
the kind of question that would be asked
is if P then Q or another type can be Q
if P for example if Labour works hard
then the boss is happy the ground gets
wet when it rains
our is in the room whenever P is in the
hotel ROM will pass if he works hard now
if when each time whenever every time
all of them belong to the same family so
we'll have the same set of rules for all
these connectives so the type of
question is if cause then effect like
here if Labour works hard this is the
cost and what is the effect that the
boss is happy or whenever cause then
effect so R is in the rule whenever P is
in the hotel or will have effect
whenever cause so this is the effect
here R is in the room and the causes
that P is in the hotel all of them mean
the same let's look at on how to solve
these questions so we'll take the first
example the ground gets wet
then it rains so the first thing we do
is we identify what is the cause and
what is the effect so it is pretty
simple that the ground getting wet is
the effect here and raining is the cause
so let's say that it rains that there is
this cause will the ground get wet yes
the ground will get wet if it does not
rain will the ground get wet I don't
know because the ground can also get wet
if I take a bucket of water and then
throw in the ground so the ground will
get wet so I don't know whether the
ground will get wet if it rains or it
does not rain now let's say that the
ground is wet can we say that it had
rained no we cannot because as I said I
it might be that somebody took a bucket
of water into the ground and that is why
the ground was wet now the ground is not
wet now we can certainly say that it had
not rained because if it had rained and
the ground definitely would have got wet
so what is this condition here in terms
of cause and effect
whenever there
this cause which is raining if there is
a cause then the effect would be
certainly there if the cause is not
there then we cannot say whether the
effect has happened or not if the effect
has occurred which means that the ground
is wet we cannot say that it is because
of this cause only this raining cause so
I put a question mark here but if the
effect has not taken place then what I
say is that there was no cause if I look
in terms of a Venn diagram I have this
effect here which is the ground getting
wet so I write in the bracket wet which
means a ground getting it and I can have
multiple causes see one would be raining
see two would be because of a bucket of
water
see three can be that there is a pipe
open in the ground and that is why is
get it's it's wet or see four can be
because of the do droplets so all these
causes will result in a ground getting
wet so in other words I have one effect
which is the ground getting wet and I
can have multiple causes C 1 C 2 and C 3
so this is pretty simple let's take
another question if the laborer works
hard then the boss is happy so what is
the cause here this is the cause the
laborer working hard this is the cause
and what is the effect that the boss is
happy so this is the effect now let's do
as we did in the previous question I say
that the laborer worked hard so I write
L for labour it means that the boss is
definitely happy so if there is a cause
there is an effect I say that the
laborer did not work hard will the boss
be happy or not
I cannot say because the boss can be
happy because probably he got married
now I say that the boss is happy so the
effect has occurred the
it mean that the labor worked hard I
cannot say that maybe the boss had his
first child so that is why he's happy
it's not necessary that you know the
labor worked hard now I take the fourth
case that the boss is not happy this
definitely means that the labor did not
work hard so again here if there was a
cause then there was this effect if
there is no cause then there is there
may be an effect or they might not be an
effect so I put a question mark here if
the effect has occurred I do not know
because of which cause so it is not
important that only because of the labor
working hard the boss was happy and if
the effect did not take place it is
definite that there was no cause none of
the causes
so obviously this cause also did not
happen so again in terms of a Venn
diagram this bigger circle is for the
effect and I can have multiple causes
the labor working hard the boss getting
married the boss having a child the boss
having an increase in revenues some
government policies might be anything so
again I have one effect and for that I
have multiple causes so the effect if it
has occurred I cannot say because of
which cause has it occurred but if one
of this causes has occurred the effect
will definitely take place so now in
logical consistency questions you are
given a main statement this is called a
main statement followed by four
statements these are the four statements
which we discussed we have to pick a
combination of two out of these four
statements which are logically correct
and are consistent with the main
statement so here this first one and
this last one are the statements which
we will pick up so summarizing I can
have many causes but one effect this is
for type 1 if when each time whenever
and every time so a cause taking place
means an effect is taking place this is
called straight logic the cause does not
take place I don't know whether the
effect will take place or not the effect
takes place I don't know whether the
cause which cause was it definitely one
cause but which one is it the one
mentioned in the question or not I don't
know but the if the effect does not take
place the cause definitely did not take
place not any of this causes so this is
called a straight negation so again with
this main diagram I have here and these
multiple causes so summarizing in terms
of sentences or a paragraph the first
takeaways if the cause occurs effect
will happen this is called a sufficient
cause that one cause is sufficient for
the effect to take place I do not need
multiple causes like draining bills is a
sufficient cause it will make the ground
wet
effect has happened means one of the
causes has occurred not the only cause
which is mentioned in the question if
cause does not occur then effect may or
may not happen we discussed before the
ground gets wet it might be because of
the rain might be because of the bucket
of water effect does not happen means no
cause has occurred it means the cause
mentioned in the question also has not
occurred this is straight negation now
let's look at the second connective here
which is only if or only when now pay at
most attention because this is where the
confusion is going to start so the type
of question is going to be only if P
then Q or Q only if P for example only
if ROM runs fast will he reach on time I
will meet you only when I come to the
Gahanna
I am born only if my mother is pregnant
so the types covered here are only if
cause then effect so the cause here is
this ROM running fast is the cause and
the effect is that he will reach on time
or effect only when cause so I will meet
you this is the effect and what is the
cause if I come to Ljubljana only when
cause then effect this is the third type
all of them mean the same the only thing
you have to identify what is the cause
here and what is the effect so let's
take an example I will meet you
only if I come to Germany so now me
coming to Germany is the cause here and
meeting you is the effect now let's say
that I met you so I represent meeting
like this letter M so I met you it means
that I definitely came to Germany let's
say I did not meet you
so did I come to Germany or not I might
have come I came to Germany I visited
Berlin I went to Munich attended
Oktoberfest and went back I didn't see
you or I would not have come to Germany
so both the things are possible so I
cannot say that I came to Germany or not
now let's say I came to Germany is it
possible that I did not meet you yes it
is because as I said earlier I might
have come to Germany for just a festival
and not meeting you so me coming to
Germany does not necessarily mean that I
met you the fourth case I did not come
to Germany so this means I definitely
did not meet you because you are staying
in Germany then how would I met you so
if we think of it in terms of cause and
effect so meeting is the effect and
coming to Germany is the cause so this
means that if the effect has occurred it
means the cause has definitely occurred
if the effect did not occur I cannot say
whether the cause occurred or not
then if the cause certainly occurred I
cannot say that the effect occurred or
not so the cause here is me coming to
Germany but it does not mean that I met
you
now if the cause did not occur it means
I did not come to Germany so the effect
will surely not occur it means I
definitely did not meet you so if we
form a diagram here as in the previous
case I have a single cause this is me
coming to Germany and it has many
effects II one is I went to Berlin e 2
is I went to Munich and attended the
Oktoberfest III is I met you so any of
these effects can take place or if I
draw a Venn diagram here this bigger
circle here will now be the cause and
I'll have lot many effects here so I
have e 1 I have a 2 I have e 3 and
similarly I might have efore and one of
these effects is meeting you so this is
entirely opposite of what we discussed
before let's take another example
I am born only if my mother is pregnant
so I am being born is the effect here
and what is the cause that my mother was
pregnant so if I am born I'll write this
as B it definitely means that my mother
was pregnant now I was not born so my
mother would could be pregnant or not it
might be that she gave birth to my
sibling my younger brother or my younger
sister so I cannot say that she was
pregnant or not now my mother is
pregnant does it mean that I will
definitely be born no I cannot say that
because as I said earlier it might be
that I have a younger sibling or an
elder sibling if my mother is not
pregnant then definitely I cannot be
born so again here if the effect has
taken place it certainly means that the
cause took place if the effect does not
take
place there may be a cause mentioned in
the question or there might be some
other cause then if the cause certainly
happened I cannot say that the effect
took place or not and if there was no
cause definitely there was no effect so
again I have a single cause and I have
many effects in 1 P 2 and P 3 similarly
I have this bigger circle here which is
the cause and then I have P 1 I have e 2
and I have III so let's summarize I have
a single cause and many effects if the
cause
took place I cannot say the effect took
place or not
if the cause did not take place the
effect certainly did not take place this
is called straight negation if the
effect took place then the cost
certainly took place this is called
straight logic in this case and if the
effect did not occur the cause might
have happened might not have happened
and then this is the Venn diagram which
we drew in the previous slides so if the
cause occurs in the effect may or may
not happen so this is not a sufficient
cause so for me being born my mother
being pregnant is not a sufficient cause
because my brother could be there a
younger brother or an elder brother who
might be born if the effect has happened
cause definitely occurred if the cause
does not occur then the effect does not
happen I cannot be born without my
mother being pregnant effect does not
happen then cause may or may not occur
cause may occur but effect may not take
place as the cause is not sufficient
which we discussed in this first case I
hope you are through with this if not
just replay this lecture from the start
till now because I know it's a little
confusing topic so let's move to this
third
type of logical connectives just if and
only if until and unless then and only
when this is the case which is nothing
but the union of the above two cases
which we've discussed and this is the
most simplest case the case also refers
to the cause being a sufficient and a
necessary cause for the effect to take
place for example if and only if he wins
the race he will get the medal until and
unless you study you will pass so for
getting the medal you have to win the
race this is the only cause and this
will definitely result in the effect
similarly you will pass only if you
study so what is the cause here that you
study and what is the effect that you
will pass or if you do not study you
will not pass so let's take an example
if and only if he wins the race will he
get the medal so what is the cause your
winning the race and getting the medal
is the effects writer he here and see
here so I represent winning the race by
are and getting the medal by M so if he
wins the race he definitely gets the
medal if he does not win the race he
will not get the medal if he get the
medal it definitely means that he won
the race and if he did not get the medal
he did not win the race so these are
pretty simple logics
so here the cause if it occurs the
effect will definitely happen if the
cause does not occur the effect will not
happen because this is the only cause is
a necessity and the sufficient cause the
only cause which is required so if the
effect occurs it means this only cause
had occurred and the effect did not
occur then it means that the cause did
not occur here if we show with the help
of a Venn diagram this C is equal to e
the cause and the effect circle are the
same because there is just one cause or
in other words I have
see and this leads to only one effect
one cause and one effect so this is what
we discussed see leads to e this is
straight logic because occur and the
effect happened because did not occur
and the effect did not happen straight
negation if the effect occurred the
cause happened if the effect did not
occur the cause did not happen and this
is how we represent in the form of a
Venn diagram so let's put the somebody
in two words cause occurs and effect
happens so this is the sufficient cause
effect happens and the cause occurred
because it's the only cause I do not
have multiple causes cause does not
occur means that the effect does not
happen as it was the only cause effect
does not happen and cause does not occur
the only cause mentioned the question
did not happen let's move on to the
fourth type of logical connective which
is either and or this is a very simple
one the type of question would be in the
form either P or Q for example either
Rahman is happy or Raghu is crazy
this is premise 1 and this is premised 2
here there is no cause-and-effect
relationship if promise 1 happens like
Ramon is happy it definitely means that
Raghu is not crazy
if promise 1 does not happen it means
that Ramon is not happy it definitely
means that Raghu is crazy so one of them
is bound to happen so as mentioned this
line below one of them is definitely
true and the other one is definitely
false let's take an example
I drink either tea or coffee so this is
the first premise drinking tea and the
second from Isis drinking coffee so if I
drink tea I definitely will not drink
coffee if I drink coffee I definitely
will not drink tea now if I don't drink
tea then I might have coffee or I might
not have coffee I'll
it's a possibility that don't have any
of them similarly if I do not drink
coffee I cannot say that I have tea or
not so this was pretty simple let's move
on to the next logical connective which
is unless here also we do not have a
cause and effect or an effect we have
just premise one and premise two so the
type of question is of the type unless P
then Q or Q unless P for example
unless Tony's the captain India will
lose the match so how do you interpret
this if P 1 is true if Tony is the
captain then India might win the match
or might lose the match this generally
happens as we see now if winning is not
the captain unless is a negative
connective if Don is not the captain
India will definitely lose the match so
if P 1 does not occur P 2 will
definitely occur now if India loses the
match like P 2 is a tick mark here I
cannot say whether Dhoni was a captain
or not but if India did not lose them as
this P 2 is a negative cross here then
definitely the only was the captain this
unless is not generally as its earlier
Lee asked connective so you just need to
get through with this one example and
then you can solve in the examination
let's move to some practice questions P
is in the room if Q is not in the hotel
so we discussed if the first connective
which we discussed now q is not in the
hotel is the cause here like we had the
ground gets wet if it rains so raining
was the cause here and P is in the room
is the effect so what did we discuss in
this case that if there is a cause if it
rains then the ground will definitely
get wet similar
if Q is not in the hotel then P is
definitely in the room if the cause does
not happen then the effect may or may
not happen if the effect happens it
might be due to some other cause so I
cannot say that the cause mentioned in
the question happened but if the effect
did not happen certainly none of the
causes happened all the cause mentioned
in the question also did not happen so
now which two combination of statements
are definitely true what they're asking
us is this the first part here which is
straight logic and this last part here
which is straight negation so kostik
mark and an effective mark means that Q
is not in the hotel and P is in the room
so let's see from here q was not in the
hotel P was in the room so I like the
cause first which is Q was not in the
hotel so DB is a correct option secondly
effect does not happen it means that the
cause did not happen so what was the
effect here P is in the room effect did
not happen means P was not in the room
so this see here P was not in the room
it means that the cause did not happen
it means that Q I'll put a not and have
to take the negation of this which means
Q is in the hotel so this is the a part
here see now take note that this
sequence also matters DB is not same as
B D and C a is not same as AC here DB is
the right answer and C is the right
answer because if the cause
takes place then the effective takes
place and if the effect does not take
place it means that the call had not
taken place so make sure that this
sequence here is correct we'll take
another example P is in the room only if
Q is not in the hotel again this is the
effect here this is the type of question
when we discuss that I will meet you
only if I come to Germany and the
is the cause yo your bun cause was
leading to many effects if you remember
that I could come to Germany and attend
the Oktoberfest go to Berlin or meet you
so one cause coming to Germany and many
things so what was the four statements
here that if the cause has taken place I
do not know whether the effect has taken
place or not it will definitely one of
the effects but the effect mentioning
the question has that occurred or not I
cannot say if the cause did not occur
like I did not go to Germany then the
effect certainly did not happen if the
effect occurred it means that the cause
had occurred I could meet you only if I
came to Germany and if the effect did
not occur I cannot say whether the cause
occurred or not so what they're asking
here is this question which is a
straight negation and sorry this one the
third one which is a straight logic so I
have to form statements for no cause
means no effect and and effect takes
place means that the cause had taken
place so no cause means the negation of
Q is not in the hotel it means that Q is
in the hotel so Q was in the hotel leads
to no effect it means that P is in the
room the negative of this means P is not
in the room so Q was in the hotel and P
was not in the room so the correct
option here is a C now here also
carefully note that C is not same as AC
AC is the answer here I will first have
a not happening cause leading to a not
happening effect what would be the
second answer the effect has taken place
it means that P is in the room
this means that Q is definitely not in
the hotel so P was in the room which is
B it means that Q was not in the hotel B
D so these are the two
conditions that follow that is all a
logical consistency I hope you enjoyed
this lecture