Concepts & Questions Based on Logical Conditions - CAT PDF Download

What are Logical Connectives?

Logical connectives are basically words or symbols which are used to form a complex sentence from two simple sentences by connecting them. 

• Some Logical Connectives are – If, Only if, When, Whenever, Unless, etc. 
• Questions based on statements formed using logical connectives are simpler than other questions of the exam so it will be beneficial to take command of this topic.

These types of sentences consist of two parts, one is Cause and one is Effect. Usually, Cause is present after the connectives.

Some examples are like:

1. If you are in navy, you have to wear uniform.
   Cause- you are in navy, Effect- you have to wear uniform.
2. If I am bored, I go for a movie.
   Cause- bored, Effect- go for a movie.

Let’s discuss all different types of questions on connectives.

(a) Logical Connective (If, then)

These statements are in the form of( If p, then q) or( q if p).

Examples:

1. If it rains then the ground gets wet.

2. Raman will pass if he works hard.

Cause-Effect Relation

• In these statements cause is a sufficient condition for effect to happen but not necessary condition.
• Let’s discuss example 1 in detail – If it rains then ground gets wet.
• In this statement firstly we’ll identify the cause and effect. “It rains is cause and ground gets wet is effect.

Now we’ll make all possible cases for understanding it clearly.

Case 1. If cause is happening, it means it is raining so obviously ground gets wet (given).
So if cause (yes) then effect (yes).

Case 2. If cause is not happening, it means its not raining so we have no idea about the condition of ground because it may be wet or not. It can get wet by some other cause also, we don’t know about that cause.
So if cause (No) then effect (may or may not be)

Case 3. If effect is happening, it means ground gets wet but we don’t know how it gets wet. We have no idea about exact cause so cause may be or may not be happened.
So if effect (Yes) then cause (may be or may not be)

Case 4. If effect is not happening, it means the ground does not get wet so we can clearly say that it has not rained because if it had rained the ground would definitely got wet.
So if effect (No) then cause is surely (No).
We can see that in this example we can say surely only in two cases (case1 & case4).
If we draw a conclusion for If and then connectives.

Conclusion (If, then):

Cause – yes; Effect – yes

Cause – no; Effect - ?

Effect – yes; Cause - ?

Effect – no; Cause – no

In these types of statements, we have SINGLE EFFECT and MULTIPLE CAUSES like ground gets wet is one effect causes may be many like rain, a bucket of water, etc.

Note: sometimes instead of ‘if’ when, whenever, everytime these connectives are used but result will be same in these cases also because meaning of statement doesn’t changes.

(b) Logical Connective (only if/when) 

These statements are in the form of (Only If p, then q) or (q, only if p). These types of connectives are very important from exam point of view.

Some examples are like:

1. I will meet you only if I come to Delhi.
2. Only if Rohit runs fast, he will catch the train.

Now first we’ll identify the cause and effect

1. Come to Delhi – cause; meet you- effect
2. runs fast – cause; catch the train- effect

Cause-Effect Relation

In these statements cause is a necessary condition for effect to happen but not a sufficient condition.
Let’s discuss example 2 in detail –. Only if Rohit runs fast, he will catch the train.
Case 1– cause yes, it means Rohit runs fast so it doesn’t mean that he will surely catch the train. Cause – yes; effect- may be may not be

Case 2 – cause no, it means Rohit doesn’t run fast so according to the statement he will catch the train only if he runs fast so surely he will not catch the train.
Cause- no; effect- no

Case3 – effect yes, it means Rohit catches the train so surely we can say he ran fast.
Effect- yes; cause- yes.

Case-4 – effect no, it means he doesn’t catch the train this doesn’t imply that he did not run fast may be due to some other reason he was not able to catch the train.
Effect- no; cause – may be may not be

Conclusion (only if):

Cause – yes; effect-?
Cause – no; effect- no
Effect – yes; cause- yes
Effect – no; cause-?

In this type of statement, there is a SINGLE CAUSE and MULTIPLE EFFECTS like running fast is a cause he can catch the train cannot catch the train these are effects.

Note- Instead of if,( when) also occur sometimes but the situation remains the same.

(c) Logical Connective (If and Only If) 

These type of sentences are union of sentences having connectives If and only If. These are the simplest in all connectives. 

It is like necessary and sufficient condition which means cause is a necessary and
sufficient condition for effect to take place.

1. If and only If he clears the pre exam, he will get selected.
2. Rahul will eat the fruit If and only If it is an apple.
3. A whole number is even If and only If its square is even.

Cause-Effect Relation

Let’s discuss all possible cases for example 1 – If and only If he clears the pre exam, he will get selected.

Cause – clears the pre exam, effect – get selected

Case 1. Cause is happening it means he cleared pre exam so surely he will get selected because given is ‘if he clears exam he will get selected’.
Cause –yes; effect – yes

Case 2. Cause is not happening it means he has not cleared pre exam so surely he will not get selected.
Cause-no; effect-no

Case 3. Effect is happening it means he selected it implies surely he has cleared his pre exam.
Effect – yes; cause – yes

Case 4. Effect is not happening it means he has not selected .By the statement ‘only if he clears the pre exam he will get selected’ we can say that he not selected means he has not cleared pre exam.
Effect – No; cause-no

Conclusion (If and only If):

Cause – yes; effect – yes
Cause – no; effect – no
Effect – yes; cause- yes
Effect – no; cause – no

In these type of statements cause is necessary and sufficient condition for effect.

Note- Instead of (If and only If) connectives (until and unless) and (when and only when) can also be used for similar conditions. Results will remain same.

(d) Logical Connective (unless)

These statements are in the form of (Unless p, q) or (q, unless p). These type of connectives do not have that much importance for exams but it is better to understand the concept. 

It is a negative type of connective which gives negative sense in the statement. In these statements there is no proper cause and effect. Only two statements are there in these type of statements.
Examples:

1. Unless I’m mistaken, John’s house is the second on the left.
2. Unless Virat is the captain, India will lose the match.

Let’s discuss example 2 in detail – . Unless Virat is the captain, India will lose the match.

Here, No cause and effect are present because it is negative statement. We can check using statements 1 and 2 directly. Virat is the captain (1) & India lose the match (2).

Case 1. If 1 is true it means Virat is the captain it doesn’t mean that India will surely win the match so we can’t say anything.
(1) – yes, (2) – may be may not be

Case 2. If 1 is false it means Virat is not the captain it means surely India will lose the match.
(1) – no, (2) – yes

Case 3. If 2 is true it means India lose the match so we can’t say anything that Virat is the captain or not. India can also lose the match when Virat is captain.
(2) – yes, (1) – may be may not be

Case 4. If 2 is not true it means India won the match so we can surely say that Virat is the captain.
(2) – no, (1) – yes

Conclusion (unless):

(1) – yes; (2) –?

(1) – no; (2) – yes
(2) – yes; (1) –?
(2) – no; (1) – yes

(e) Logical Connective (Either or)

These statements are in the form of (either p or q). These are very simple statements. P and q are two statements. No cause and effect is present in this case.

Examples:

1. I drink either green tea or juice.
2. Either Ronak is intelligent or Raman is foolish.

In these types of statements clearly, if one statement is false then the second is true and if one is true second is false.

For Example 1:

If I drink green tea it means surely I don’t drink juice. And If I drink juice it means surely I don’t drink green tea. No need to make cases here we can directly write conclusions.

Conclusion (Either, or)-

(1) – yes; (2) – no
(1) – no; (2) – yes
(2) – yes; (1) – no
(2) – no; (1) – yes

Note- In these type of statements clearly one of the statements is definitely true and one is definitely false.

Directions to Solve Questions Based on Logical Conditions

In each of the following questions, two statements numbered I and II are given. There may be cause and effect relationship between the two statements. These two statements may be the effect of the same cause or independent causes. These statements may be independent causes without having any relationship. Read both the statements in each question and mark your answer as

• (A) If statement I is the cause and statement II is its effect;
• (B) If statement II is the cause and statement I is its effect;
• (C) If both the statements I and II are independent causes;
• (D) If both the statements I and II are effects of independent causes; and
• (E) If both the statements I and II are effects of some common cause.

Q.1. Statements:

I. The prices of petrol and diesel in the domestic market have remained unchanged for the past few months.

II. The crude oil prices in the international market have gone up substantially in the last few months.

A.    Statement I is the cause and statement II is its effect

B.    Statement II is the cause and statement I is its effect

C.    Both the statements I and II are independent causes

D.    Both the statements I and II are effects of independent causes

E.    Both the statements I and II are effects of some common cause

Answer: Option D 

Explanation: The prices of petrol and diesel being stagnant in the domestic market and the increase in the same in the international market must be backed by independent causes.

I. The government has recently fixed the fees for professional courses offered by the unaided institutions which are much lower than the fees charged last year.

II. The parents of the aspiring students launched a severe agitation last year protesting against the high fees charged by the unaided institutions.

A.    Statement I is the cause and statement II is its effect

B.    Statement II is the cause and statement I is its effect

C.    Both the statements I and II are independent causes

D.    Both the statements I and II are effects of independent causes

E.    Both the statements I and II are effects of some common cause

Answer: Option B

Explanation: The parents' protest against high fees being charged by the institutions led the government to interfere and fix the fees at a more affordable level.

Q.3. Statements: 

I. The Reserve Bank of India has recently put restrictions on few small banks in the country.

II. The small banks in the private and co-operative sector in India are not in a position to withstand the competition of the bigger in the public sector.

A.    Statement I is the cause and statement II is its effect

B.    Statement II is the cause and statement I is its effect

C.    Both the statements I and II are independent causes

D.    Both the statements I and II are effects of independent causes

E.    Both the statements I and II are effects of some common cause

Answer: Option B

Explanation: The inability of the small banks to compete with the bigger ones shall not ensure security and good service to the customers, which is an essential concomitant that has to be looked into by the Reserve Bank. I seems to be a remedial step for the same.

Q.4. Statements:

I. All the schools in the area had to be kept closed for most part of the week.

II. Many parents have withdrawn their children from the local schools.

A.    Statement I is the cause and statement II is its effect

B.    Statement II is the cause and statement I is its effect

C.    Both the statements I and II are independent causes

D.    Both the statements I and II are effects of independent causes

E.    Both the statements I and II are effects of some common cause

• Answer: Option D
• Explanation: Closing the schools for a week and the parents withdrawing their wards from the local schools are independent issues, which must have been triggered by different individual causes.

India has surpassed the value of tea exports this year over all the earlier years due to an increase in demand for quality tea in the European market.

There is an increase in demand of coffee in the domestic market during the last two years.

A.    Statement I is the cause and statement II is its effect

B.    Statement II is the cause and statement I is its effect

C.    Both the statements I and II are independent causes

D.    Both the statements I and II are effects of independent causes

E.    Both the statements I and II are effects of some common cause

Answer: Option C

Explanation: The two statements discuss two separate statistical and generalized results.