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The Parity command returns the Boolean expression corresponding to the parity function on a set of variables: that is, the function which is true if and only if an odd number of inputs are true.

The parity function is symmetric in its inputs: the order of true or false values is unimportant, only the number of true inputs.

$\mathrm{with}\left(\mathrm{Logic}\right)\:$

$\mathrm{Parity}\left(\mathrm{true}\,\mathrm{false}\,\mathrm{true}\right)$

$\mathrm{false}$

$\mathrm{Parity}\left(\mathrm{`\$`}\left(x\,m\right)\,\mathrm{`\$`}\left(y\,n\right)\,x\right)\mathbf{assuming}m::\mathrm{even},n::\mathrm{odd}$

$\mathrm{Parity}\left(x\,y\right)$

$p≔\mathrm{Parity}\left(x\,y\,z\,w\right)$

$p≔\mathrm{Parity}\left(w\,x\,y\,z\right)$

$\mathrm{length}\left(\mathrm{Convert}\left(p\,\mathrm{form}=\mathrm{CNF}\right)\right)$

$280$

$\mathrm{length}\left(\mathrm{Convert}\left(p\,\mathrm{form}=\mathrm{DNF}\right)\right)$

$287$

The Logic[Parity] command was introduced in Maple 2017.

For more information on Maple 2017 changes, see Updates in Maple 2017 .