Truth table for $$$\left(p \rightarrow q\right) \leftrightarrow \left(\neg q \rightarrow \neg p\right)$$$
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Find the truth table for $$$\left(p \rightarrow q\right) \leftrightarrow \left(\neg q \rightarrow \neg p\right)$$$.
Answer
$$$p$$$ | $$$q$$$ | $$$p \rightarrow q$$$ | $$$\neg q$$$ | $$$\neg p$$$ | $$$\neg q \rightarrow \neg p$$$ | $$$\left(p \rightarrow q\right) \leftrightarrow \left(\neg q \rightarrow \neg p\right)$$$ |
True | True | True | False | False | True | True |
True | False | False | True | False | False | True |
False | True | True | False | True | True | True |
False | False | True | True | True | True | True |