Test: Set Theory- 2 - CAT MCQ

We can simply solve this problem by using the following mathematical process.

A power set is defined as the set or group of all subsets for any given set, including the empty set.  A set that has 'n' elements has 2n subsets in all.

The power set is denoted by the notation P(S) and the number of elements of the power set is given by 2n.

In the given set, the number of elements is 2

Therefore, in the power set, the number of elements will be

Hence, The number of elements in the power set of the set {{a,b},c} is 4.

The correct answer is D as
 R = ((1, 1), (3, 1), (2, 3), (4, 2))
RoR=R²=((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 R² similarly check for all.
like (4,2) (2,3)=(4,3)in R²

Let X was the people who speaks all three languages.
Total number of people = (Hindi + English + Kannad) - (Hindi and English + Hindi and Kannad + Kannad and English) + X

28 = (15 + 22 + 18) - (9 + 11 + 13) +X

X = 28 - 55 + 33

X = 6.

The correct answer is C as
Let,the number of voters (experts) be denoted as x
A/Q
 X/2+2x/3-10+6=x
7x/6-4=x
7x-24=6x
x=24
 

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
=>(x-y)+(y-z) = m(q+q')
=> x - z = m(q + q'), q + q' ∈ I
(x,z) ∈ R
=> R is transitive.
Hence the relation is equivalence relation.