Answer :
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]
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]
