Question

Universal relation defined on AxB is symmetric, where A is not a subset of B

• A. True
• B. False

Answer 1

The correct option is B

False

Let us take an example to find this out. A = {1} and B = {2}, both satisfying the given condition that A is not a subset of B. To find the universal relation, we will find the cartesian product since both are same. The cartesian product AB is nothing but {(1,2)}. This is also the universal relation. By observing this we see that there is no element (2,1) while we have element (1,2) which violates the condition of symmetric relation, that is if there is an element (a,b ) then there should be an element (b, a) for a relation to be symmetric. To prove some statement is wrong is wrong we just need an example which contradicts that. So the answer is false