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