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This mock test of Test: Set Theory- 1 for CAT helps you for every CAT entrance exam.
This contains 10 Multiple Choice Questions for CAT Test: Set Theory- 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B = Ø

Then (pick the TRUE statement)

Solution:

The correct answer is B asLet A={1,2,3

B={4,5}

C={1,6,7}

now

A∩B=∅

B∩C=∅

B∩C=∅ but

A∩C≠∅

R is not transitive.

A∩A=A

R is not reflexive.

A∩B=B∩A

R is symmetric

So,

A is false as

R is not reflexive or transitive

B is true.

C is false because

R is not transitive or reflexive

D is false because

R is symmetric

QUESTION: 2

The binary relation S = Φ (empty set) on set A = {1, 2,3} is

Solution:

**Explanation:**

**Reflexive**: A relation is reflexive if every element of set is paired with itself. Here none of the element of A is paired with themselves, so S is not reflexive.**Symmetric**: This property says that if there is a pair (a, b) in S, then there must be a pair (b, a) in S. Since there is no pair here in S, this is trivially true, so S is symmetric.**Transitive**: This says that if there are pairs (a, b) and (b, c) in S, then there must be pair (a,c) in S. Again, this condition is trivially true, so S is transitive.**Thus, option (D) is correct.**

QUESTION: 3

Which of the following sets are null sets ?

Solution:

There are some sets that do not contain any element at all. For example, the set of months with 32 days. We call a set with no elements the null or empty set. It is represented by the symbol { } or Ø.

QUESTION: 4

Number of subsets of a set of order three is

Solution:

Number of subset = 2^{n}

order 3 = 2^{3}

⇒ 8

QUESTION: 5

"n/m" means that n is a factor of m, then the relation T is

Solution:

′/′ is reflexive since every natural number is a factor of itself that in n/n for n∈N.

′/′ is transitive if n is a factor of m and m is a factor of P, then n is surely a factor of P.

However, ′/′ is not symmetric.

example, 2 is a factor of 4 but 4 is not a factor of 2.

QUESTION: 6

The number of elements in the Power set P(S) of the set S = [ [ Φ] , 1, [ 2, 3 ]] is

Solution:

QUESTION: 7

If A and B are sets and A∪ B= A ∩ B, then

Solution:

QUESTION: 8

Let S be an infinite set and S_{1}, S_{2}, S_{3}, ..., S_{n} be sets such that S_{1} ∪S_{2} ∪S_{3}∪ .......S_{n} = S then

Solution:

Let S = S1 ∪ S2 ∪ S3 ∪ .... Sn .

For S to be infinite set, atleast one of sets S_{i} must be infinite,

if all S_{i} were finite, then S will also be finite.

QUESTION: 9

If X and Y are two sets, then X ∩ (Y ∪ X) C equals

Solution:

QUESTION: 10

If f : X -> Y and a, b ⊆ X, then f (a ∩ b) is equal to

Solution:

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