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The number of elements in the power set of the set {{a, b}, c} is
If R = ((1, 1), (3, 1), (2, 3), (4, 2)), then which of the following represents R2, where R2 is R composite R?
The correct answer is D as
R = ((1, 1), (3, 1), (2, 3), (4, 2))
RoR=R^{2}=((1, 1), (3, 1), (2, 3), (4, 2))((1, 1), (3, 1), (2, 3), (4, 2))
=((1, 1), (3, 1), (2, 1), (4, 3))
take the first set (1,1) then take the second element of this subset check in the other set R is there any starting with 1 if yes then take its second element and make a subset in R^{2} similarly check for all.
like (4,2) (2,3)=(4,3)in R^{2}
In a room containing 28 people, there are 18 people who speak English, 15 people who speak Hindi and 22 people who speak Kannada, 9 persons speak both English and Hindi, 11 persons speak both Hindi and Kannada where as 13 persosn speak both Kannada and English. How many people speak all the three languages ?
If f : R >R defined by f(x) = x2 + 1, then values of f 1 (17) and f 1(3) are respectively
In a beauty contest, half the number of experts voted for Mr. A and two thirds voted for Mr. B. 10 voted for both and 6 did not vote for either. How many experts were there in all ?
The correct answer is C as
Let,the number of voters (experts) be denoted as x
A/Q
X/2+2x/310+6=x
7x/64=x
7x24=6x
x=24
Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered pairs (a, b) are there with a ∈ A and b ∈ B ?
The set of all Equivalence classes of a set A of cardinality C
Let Z denote the set of all integers.
Define f : Z —> Z by
f(x) = {x / 2 (x is even)
0 (x is odd)
then f is
Let R be a relation "(x y) is divisible by m", where x, y, m are integers and m > 1, then R is
a) Since x  x = 0, m
=> x  x is divisible by m
(x,x) ∈ R
=> R is reflexive
b) Let (x,y) ∈ R
=> x  y = mq for some q ∈ I
=> y  x = m(q)
y  x is divisible by m
(y,x) ∈ R
=> R is symmetric.
c) Let (x,y) and (y,z) ∈ R
=> x  y is divisible by m and y  z is divisible by m
=> x  y = mq and y  z = mq' for some q, q' ∈ I
=>(xy)+(yz) = m(q+q')
=> x  z = m(q + q'), q + q' ∈ I
(x,z) ∈ R
=> R is transitive.
Hence the relation is equivalence relation.
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