(p → q) ∧ (p → r) is logically equivalent top ∧ (q ∨ r)p → (q ∧ r) p ∨ (q ∧ r) p → (q ∨ r)
Question
(p → q) ∧ (p → r) is logically equivalent to
p ∧ (q ∨ r)
p → (q ∧ r)
p ∨ (q ∧ r)
p → (q ∨ r)
Solution
The statement seems to be a mix of different logical expressions, and it's not clear what the exact question is. However, I can explain the logical expressions mentioned:
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(p → q) ∧ (p → r): This means "if p then q" and "if p then r". In other words, p implies both q and r.
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p ∧ (q ∨ r): This means "p and (either q or r)". In other words, p must be true, and either q or r (or both) must be true.
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p → (q ∧ r): This means "if p then both q and r". In other words, if p is true, then both q and r must be true.
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p ∨ (q ∧ r): This means "either p or both q and r". In other words, either p is true, or both q and r are true.
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p → (q ∨ r): This means "if p then either q or r". In other words, if p is true, then either q or r (or both) must be true.
Please clarify the question so I can provide a more specific answer.
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