GATE 1998
March 18, 2025GATE 1998
March 18, 2025GATE 1998
| Question 7 |
Let R1 and R2 be two equivalence relations on a set. Consider the following assertions:
- (i) R1 ∪ R2 is an equivalence relation
(ii) R1 ∩ R2 is an equivalence relation
Which of the following is correct?
| Both assertions are true | |
| Assertion (i) is true but assertion (ii) is not true | |
| Assertion (ii) is true but assertion (i) is not true | |
| Neither (i) nor (ii) is true |
Question 7 Explanation:
If R1 and R2 be two equivalence relations on a set ‘S’ then the transitive property tells
(i) R1 ∩ R2 is also transitive.
(ii) R1 ∪ R2 is need not to be transitive.
(i) R1 ∩ R2 is also transitive.
(ii) R1 ∪ R2 is need not to be transitive.
Correct Answer: C
Question 7 Explanation:
If R1 and R2 be two equivalence relations on a set ‘S’ then the transitive property tells
(i) R1 ∩ R2 is also transitive.
(ii) R1 ∪ R2 is need not to be transitive.
(i) R1 ∩ R2 is also transitive.
(ii) R1 ∪ R2 is need not to be transitive.