Logical Equivalence of the Conditional

Logic Level 2

Which of the following statements is equivalent to $P\Rightarrow Q$ ?

P\Rightarrow (\sim Q

)

(\sim Q)\Rightarrow P

(\sim Q)\Rightarrow (\sim P

)

(\sim P)\Rightarrow (\sim Q

)

Q\Rightarrow P

1 solution

Shawn Franchi
Apr 15, 2016

The truth table for the implication $P\Rightarrow Q$ is given as follows:

$P$	$Q$	$P\Rightarrow Q$
TRUE	TRUE	TRUE
TRUE	FALSE	FALSE
FALSE	TRUE	TRUE
FALSE	FALSE	TRUE

We note that the implication is only false in the case where $P$ is true and $Q$ is false. This is exactly what restriction is meant for the truth values by $(\sim Q)\Rightarrow (\sim P)$ , which is called the contrapositive of the original implication $P\Rightarrow Q$ .

Logical Equivalence of the Conditional

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