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p → q is logically equivalent to

Question

p → q is logically equivalent to

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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:

  1. "p → q" is a conditional statement, which means "if p then q".

  2. This can be interpreted as "either p is false, or q is true".

  3. In logical notation, "p is false" is represented as "¬p" and "q is true" is simply "q".

  4. The word "or" in logic is represented as "∨".

  5. 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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