Duality
Category : JEE Main & Advanced
Definition : Two compound statements \[{{S}_{1}}\] and \[{{S}_{2}}\] are said to be duals of each other if one can be obtained from the other by replacing \[\wedge \]by \[\vee \] and \[\vee \]by \[\wedge \].
t (tautology) or c (contradiction), then to obtain its dual we replace t by c and c by t in addition to replacing \[\wedge \]by \[\vee \]and \[\vee \]by \[\wedge \].
(i) \[\tilde{\ }S(p,q)\equiv {{S}^{*}}(\tilde{\ }p,\tilde{\ }q)\]
(ii) \[\tilde{\ }{{S}^{*}}(p,q)\equiv S(\tilde{\ }p,\tilde{\ }q)\]
(i) \[\tilde{\ }S({{p}_{1}},{{p}_{2}},....,{{p}_{n}})\equiv {{S}^{*}}(\tilde{\ }{{p}_{1}},\tilde{\ }{{p}_{2}},....,\tilde{\ }{{p}_{n}})\]
(ii) \[\tilde{\ }{{S}^{*}}({{p}_{1}},{{p}_{2}},....,{{p}_{n}})\equiv S(\tilde{\ }{{p}_{1}},\tilde{\ }{{p}_{2}},....,\tilde{\ }{{p}_{n}})\]
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