Classical

Set Theory and Algebra MCQ - Sets

61:  

 A Relation R is defined on the set of integers as xRy if (x + y) is even. Which of the following statements is TRUE?

A.

R is not an equivalence relation

B.

R is an equivalence relation having one equivalence class

C.

R is an equivalence relation having two equivalence classes

D.

R is an equivalence relation having three equivalence classes

 
 

Option: C

Explanation :

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62:  

 Let P(S) denote the power set of set S. Which of the following is always TRUE ?

A.

P(P(S)) = P(S)

B.

P(S)  ∩ S = P (S)

C.

P(S)  ∩ P(P(S))  = [ φ ]

D.

∉ P(S)

 
 

Option: C

Explanation :

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63:  

If R be a symmetric and transitvie relation on a set A, then

A.

R is reflexive and hence an equivalence relation

B.

R is reflexive and hence a partial order

C.

R is not reflexive and hence not an equivalence relation

D.

None of these

 
 

Option: D

Explanation :

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64:  

The number of binary relations on a set with n elements is 

A.

n2

B.

2n^2

C.

2n

D.

None of these

 
 

Option: B

Explanation :

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65:  

If A and B be sets and AC and Bc denote the complements of the sets A and B, then set (A — B)  (B — A)  (A   ∩ B) is equal to

A.

∪ B

B.

A∪ Bc

C.

 B

D.

Ac  Bc

 
 

Option: A

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∪(B — A)(A B) is equal to

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