The negation of the statement "For all real n | vedclass

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(C) The given statement is a universal quantification: "For all $x, y \in \mathbb{R}, x+y=y+x$." To find the negation of a statement involving the uni

Vedclass · Accepted Answer

For some real numbers $x$ and $y, x+y 
eq y+x$

Vedclass · Answer

(C) The given statement is a universal quantification: "For all $x, y \in \mathbb{R}, x+y=y+x$." To find the negation of a statement involving the universal quantifier "For all" $(\forall)$,we replace it with the existential quantifier "There exists" (or "For some") and negate the predicate. The negation of "For all $x$ and $y, P(x, y)$" is "There exist $x$ and $y$ such that $
eg P(x, y)$." Here,the predicate $P(x, y)$ is $x+y=y+x$. The negation of $x+y=y+x$ is $x+y 
eq y+x$. Therefore,the negation of the statement is "For some real numbers $x$ and $y, x+y 
eq y+x$."

The negation of the statement "For all real numbers $x$ and $y, x+y=y+x$" is

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