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It assumes that $P$ and $Q$ are correct mathematical expressions. The sentence $P\rightarrow Q$ has associated sentences

$Q\rightarrow P$ $\hspace{15mm}$reciprocal of $\hspace{20mm}P\rightarrow Q$;

$\neg P\rightarrow \neg Q$ $\hspace{8mm}$ inverse of $\hspace {25mm}P\rightarrow Q$;

$\neg Q\rightarrow \neg P$ $\hspace{8mm}$ counter-reciprocal of $\hspace {7mm} P\rightarrow Q$.

Pairwise have the same truth table. What are these partners?

[Hint. Use truth tables]

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    Hint: use the hint – 2017-01-28
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    Have you built and compared the truth tables of the expressions in the first line for example ? Do you want us to work at your place ? – 2017-01-28
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    Besides, that title is not really a title... don't you think ? – 2017-01-28
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    What have you tried? Where did you get stuck? Don't just ask us to do your homework for you . . . – 2017-01-28

1 Answers 1

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Note that the pair "P → Q and its counter-relationship" have the same truth table

Idem with the "reciprocal and inverse pair of P → Q"

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    I would not like to interfere with your freedom to answer to anybody, but as you are new to this site, I do not encourage you to answer to this type of OP: there is a fraction (10%-20%) of the askers who wait that we provide the answer on a silver tray. This guy evidently belongs to this category. In the ideal situations, some hints are enough. – 2017-01-28