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Is the implication $$A \implies \left(B \oplus C\right)$$ logically equivalent to $$\left(A \implies B\right) \oplus \left(A \implies C\right),$$ where $\oplus$ is the logical XOR operator, and $B$ and $C$ are mutually exclusive conditions?

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No. Consider the case where $A$ and $B$ are false, and $C$ is true. The first statement is true (since "false implies $X$" is always true), but the second is false (since both implications are true).

florence
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