Classical

Set Theory and Algebra MCQ - Algebra

21:  

 Which of the following statements is false ?

A.

If R is relexive, then R ∩ R-1 ≠ φ

B.

 R ∩ R-1 ≠ φ   =>R  is anti-symmetric.

C.

If R, R' are equivalence relations in a set A, then  R ∩ R'  is also an equivalence relation in A.

D.

If R, R' are relexive relations in A, then R - R' is reflexive

 
 

Option: D

Explanation :


22:  

 If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3}  then R . R (= R2) is

A.

R itself

B.

{(1, 2),(1, 3),(3, 3)}

C.

{(1, 3),(2, 3),(3, 3)}

D.

{(2, 1),(1, 3),(2, 3)}

 
 

Option: C

Explanation :




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