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Why is the contrapostive of an implication equivalent to its normal truth table? i.e. why is this the case:

$$ \begin{array}{c|l|c} p & q & \text~p \implies \text~q \\ \hline 1 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \\ 0 & 0 & 1 \\ \end{array} $$

Given that the nomal implication table is:

$$ \begin{array}{c|l|c} B & A & B \implies A \\ \hline 1 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \\ 0 & 0 & 1 \\ \end{array} $$

Specifically, in the first table and first row: p = 1, thus ~p = 0; q = 0, thus ~q = 1. Given these, if one enters these values ( B=0 and A=1) into the second, basic implication table, then the statement is true.

An example would help. I cannot grasp the meaning so I can't really think of any good examples.

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    you sure about your resource ?2012-12-11

2 Answers 2