Originally Posted by

**sktsasus**
**Below are listed several pairs of sentences, both in propositional logic and in predicate logic. In each pair, one of the sentences implies the other. Decide which of the two logically implies the other one, and give justification for your answer.**

**(a) Q; P ⇒ Q**

**(b) S ∧ (P ⇒ Q) ∧ ((星) ⇒ Q); Q ∨ R**

I tried to approach each of these using reasoning rather than truth tables. But I must admit it ended up being more of a guessing game than anything. So I need some help.

For a), I thought that Q implies P ⇒ Q because when in some cases when P ⇒ Q is true, Q is still false.

For b), I thought Q ∨ R implies S ∧ (P ⇒ Q) ∧ ((星) ⇒ Q) because Q is present in the larger statement and R is not so I thought the smaller statement could just be considered as Q only.

However, my reasoning is not very strong for either.

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