Truth table for (((m => j) ∧ ((k ∧ d) ∧ c)) => m) => (((k ∧ d) ∧ c) => j)

The calculator will generate the truth table for the given logic formula $$$\left(\left(\left(m \rightarrow j\right) \wedge \left(\left(k \wedge d\right) \wedge c\right)\right) \rightarrow m\right) \rightarrow \left(\left(\left(k \wedge d\right) \wedge c\right) \rightarrow j\right)$$$, with steps shown.

Related calculator: Boolean Algebra Calculator

Expression:

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Ordering:

Leave empty for default ordering or specify variables like p,r,q (comma-separated).

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Your Input

Find the truth table for $$$\left(\left(\left(m \rightarrow j\right) \wedge \left(\left(k \wedge d\right) \wedge c\right)\right) \rightarrow m\right) \rightarrow \left(\left(\left(k \wedge d\right) \wedge c\right) \rightarrow j\right).$$$

Answer

$$$m$$$	$$$j$$$	$$$k$$$	$$$d$$$	$$$c$$$	$$$m \rightarrow j$$$	$$$k \wedge d$$$	$$$\left(k \wedge d\right) \wedge c$$$	$$$\left(\left(k \wedge d\right) \wedge c\right) \rightarrow j$$$	$$$\left(m \rightarrow j\right) \wedge \left(\left(k \wedge d\right) \wedge c\right)$$$	$$$\left(\left(m \rightarrow j\right) \wedge \left(\left(k \wedge d\right) \wedge c\right)\right) \rightarrow m$$$	$$$\left(\left(\left(m \rightarrow j\right) \wedge \left(\left(k \wedge d\right) \wedge c\right)\right) \rightarrow m\right) \rightarrow \left(\left(\left(k \wedge d\right) \wedge c\right) \rightarrow j\right)$$$
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False	False	False	False	True	True	False	False	True	False	True	True
False	False	False	False	False	True	False	False	True	False	True	True

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Truth table for $$$\left(\left(\left(m \rightarrow j\right) \wedge \left(\left(k \wedge d\right) \wedge c\right)\right) \rightarrow m\right) \rightarrow \left(\left(\left(k \wedge d\right) \wedge c\right) \rightarrow j\right)$$$

Your Input

Answer