The relation R defined on the set A = {1, 2, | vedclass

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(D) The relation is defined as $R = \{(x, y) : x, y \in A 	ext{ and } |x^2 - y^2| < 16\}$.We check the given options to see if all pairs in a set sat

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None of these

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(D) The relation is defined as $R = \{(x, y) : x, y \in A 	ext{ and } |x^2 - y^2| We check the given options to see if all pairs in a set satisfy the condition $|x^2 - y^2| For option $A$: $|1^2 - 1^2| = 0 $|2^2 - 1^2| = |4 - 1| = 3 $|3^2 - 1^2| = |9 - 1| = 8 $|4^2 - 1^2| = |16 - 1| = 15 $|2^2 - 3^2| = |4 - 9| = 5 All pairs in option $A$ satisfy the condition. However,a relation $R$ is a subset of $A 	imes A$. The question asks for the relation $R$ itself,which contains all such pairs. Since the options provided are subsets of $R$,and option $A$ is a valid subset,we evaluate if it represents the full relation. Actually,$R$ contains many more pairs (e.g.,$(1, 2), (5, 5)$). Given the structure,option $A$ is a subset of $R$. Since none of the options represent the complete set $R$,the correct choice is $D$.

The relation $R$ defined on the set $A = \{1, 2, 3, 4, 5\}$ by $R = \{(x, y) : |x^2 - y^2| < 16\}$ is:

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