Truth table for $$$\left(\left(p \wedge \left(g \vee \neg p\right)\right) \wedge \left(g \rightarrow c\right)\right) \rightarrow \left(g \wedge c\right)$$$

The calculator will generate the truth table for the given logic formula $$$\left(\left(p \wedge \left(g \vee \neg p\right)\right) \wedge \left(g \rightarrow c\right)\right) \rightarrow \left(g \wedge c\right)$$$, with steps shown.

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Your Input

Find the truth table for $$$\left(\left(p \wedge \left(g \vee \neg p\right)\right) \wedge \left(g \rightarrow c\right)\right) \rightarrow \left(g \wedge c\right)$$$.

Answer

$$$p$$$$$$g$$$$$$c$$$$$$\neg p$$$$$$g \rightarrow c$$$$$$g \wedge c$$$$$$g \vee \neg p$$$$$$p \wedge \left(g \vee \neg p\right)$$$$$$\left(p \wedge \left(g \vee \neg p\right)\right) \wedge \left(g \rightarrow c\right)$$$$$$\left(\left(p \wedge \left(g \vee \neg p\right)\right) \wedge \left(g \rightarrow c\right)\right) \rightarrow \left(g \wedge c\right)$$$
TrueTrueTrueFalseTrueTrueTrueTrueTrueTrue
TrueTrueFalseFalseFalseFalseTrueTrueFalseTrue
TrueFalseTrueFalseTrueFalseFalseFalseFalseTrue
TrueFalseFalseFalseTrueFalseFalseFalseFalseTrue
FalseTrueTrueTrueTrueTrueTrueFalseFalseTrue
FalseTrueFalseTrueFalseFalseTrueFalseFalseTrue
FalseFalseTrueTrueTrueFalseTrueFalseFalseTrue
FalseFalseFalseTrueTrueFalseTrueFalseFalseTrue