Question

How many elements will be there in the universal relation defined on the set A = {1,4, 9}

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Answer 1

Universal relation is a relation in which all elements are connected to each other. We also saw that universal relation and cartesian product are same. In a cartesian product between two sets with m and n number of elements, there will be m $\times$ n elements. So the number of elements in the cartesian product of A $\times$ A will be equal to 3 $\times$ 3 or 9. This is same as the number of elements in a universal relation. So the answer is 9