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p → q is logically equivalent to ________ans.¬p ∧ qp ∨ ¬q¬p ∨ q¬p ∨ ¬q Previous Marked for Review Next

Question

p → q is logically equivalent to ________

  • ans.
    • ¬p ∧ q
    • p ∨ ¬q
    • ¬p ∨ q
    • ¬p ∨ ¬q
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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 logical statement saying "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 written as "¬p" and "or" is written as "∨".

  4. So, "either p is false, or q is true" is written as "¬p ∨ q".

Therefore, "p → q" is logically equivalent to "¬p ∨ q".

This problem has been solved

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