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What is the inverse of the statement below?

[tex]\[x = y\][/tex]

A. \(\neg x \Rightarrow \neg y\)

B. \(y \Rightarrow x\)

C. \(\neg x \Rightarrow y\)

D. [tex]\(\neg y \Rightarrow \neg x\)[/tex]

Sagot :

GinnyAnsweridn
To determine the inverse of the statement \(x = y\), we need to understand the concept of logical statements and their inverses.

A logical implication "if \(A\), then \(B\)" is written as \(A \Rightarrow B\). The inverse of this statement is "if not \(B\), then not \(A\)", written as \(\neg B \Rightarrow \neg A\).

For the given statement \(x = y\), we can interpret it as a logical implication:
- \(x \Rightarrow y\).

Now, the inverse of \(x \Rightarrow y\) is:
- \(\neg y \Rightarrow \neg x\)

Hence, the correct answer for the inverse of the statement \(x = y\) is:
[tex]\[ \text{D. } \neg y \Rightarrow \neg x \][/tex]
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