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I am confused with the equivalence:(p→r)∨(q→r)≡(p∧q)→r.I checked that truth tables supports it but I cannot imagine an example which justifies it.

Suppose: p says “It is raining”, q says “It is snowing” and r says: “we will close”. So(p→r)∨(q→r)becomes “if it is raining then we will close or if it snows then we will close”. Is this not same as saying If it rains or snows or both then we will close? Then why(p∧q)→rand not(p∨q)→r ?

Thanks in advance.

* Also, can you pls. provide an example for p → q ≡ ¬p ∨ q ?

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# I Conditional Proposition Equivalence

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