4. Logical equivalence

Logical equivalence

Logically equivalent

Two formulae that have the same truth values in all possible cases are logically equivalent, denoted by $p\equiv q$.

For example, $p\to q$ and $\neg p\vee q$.

$p$	$q$	$\neg p$	$p\to q$	$\neg p\vee q$
T	T	F	T	T
T	F	F	F	F
F	T	T	T	T
F	F	T	T	T

This is not a logical connective but just a shorthand.

$p$ and $q$ are logically equivalent if and only if the formula $p⟺q$ is a [[Tautology|tautology]].

Link to original

List of well-known equivalences

You do not need to memorise these for the exam.

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