Question

When does $\mathit{s}\mathbf{*}\mathbf{=}\mathit{s}$, where s is a compound proposition

Short answer

$s*=s$when the compound proposition contains only thesame propositions.

Step-by-step solution

Step1:Definition of dual

The dual of a proposition which contains only the logical operators $\vee ,\wedge ,\neg$, is the compound proposition obtained by replacing each $\wedge$by $\vee$, each $\vee$by $\wedge$ , each by , and each T by F .The dual of S is denoted by $s*$.

Step 2:  s*=swhen two propositions are same

$s*=s$iswhen the compound proposition is composed only of thesame propositions.

For example, \(p \wedge p = p \vee p\).