Let S = {0, 1, 2, 3, ldots, 100}. The number | vedclass

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(D) Given the set $S = \{0, 1, 2, 3, \ldots, 100\}$.We need to find the number of pairs $(x, y)$ such that $x, y \in S$,$x 
eq y$,and $x + y = 100$.P

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$100$

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(D) Given the set $S = \{0, 1, 2, 3, \ldots, 100\}$.We need to find the number of pairs $(x, y)$ such that $x, y \in S$,$x 
eq y$,and $x + y = 100$.Possible pairs $(x, y)$ satisfying $x + y = 100$ are:$(0, 100), (1, 99), (2, 98), \ldots, (49, 51), (50, 50), (51, 49), \ldots, (100, 0)$.There are $101$ such pairs in total.We are given the condition $x 
eq y$.In the pair $(50, 50)$,we have $x = y = 50$,so this pair must be excluded.All other pairs $(x, y)$ satisfy $x 
eq y$.The number of pairs where $x 
eq y$ is $101 - 1 = 100$.However,the question asks for the number of ways of selecting $x$ and $y$ such that $x+y=100$ and $x 
eq y$. Since the order of selection is implied by the distinct variables $x$ and $y$,we count all valid ordered pairs.There are $50$ pairs where $x  y$ (i.e.,$(51, 49), \ldots, (100, 0)$).Total ways $= 50 + 50 = 100$.

Let $S = \{0, 1, 2, 3, \ldots, 100\}$. The number of ways of selecting $x, y \in S$ such that $x \neq y$ and $x + y = 100$ is

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