p → q is logically equivalent to
Question
p → q is logically equivalent to
Solution
The statement "p → q" is logically equivalent to "¬p ∨ q". This is known as the material implication in logic.
Here's the step by step explanation:
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"p → q" is a conditional statement, which means "if p then q".
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This can be interpreted as "either p is false, or q is true".
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In logical notation, "p is false" is represented as "¬p" and "q is true" is simply "q".
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The word "or" in logic is represented as "∨".
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Therefore, "either p is false, or q is true" is represented as "¬p ∨ q".
So, "p → q" is logically equivalent to "¬p ∨ q".
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