| Assertion: The relation R in the set A = {1, 2, 3, 4, 5, 6} defined as R = {(x, y) : y is divisible by x} is an equivalence relation. |
| Reason: A relation R on the set A is equivalence if it is reflexive, symmetric and transitive. |
A) Both A and R are individually true and R is the correct explanation of A.
B) Both A and R are individually true and R is not the correct explanation of A.
C) 'A' is true but 'R' is false
D) 'A' is false but 'R' is true
E) Both A and R are false.
Correct Answer: D
Solution :
Given R = {(x, y) : y is divisible by x} = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 4), (2, 6), (3, 6)} Clearly \[\left( 1,\,\,2 \right)\in \,R\] but \[\left( 2,\,\,1 \right)\notin \,R\] \[\Rightarrow \]R is not symmetric Relation \[\Rightarrow \]R is not equivalence relation \[\Rightarrow \]Assertion [A] is not true Also Reason R is true (Definition of equivalence relations) Hence option [D] is the correct answer.
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