(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let p(n) and q(n) be predicates. For each pair of statements below, determine

whether the two statments are logically equivalent. Justify your answers.

a)

(i) ∀n (p(n) ∧ q(n))

(ii) (∀n p(n)) ∧ (∀n q(n))

b)

(i) ∃n st (p(n) ∧ q(n))

(ii) (∃n st p(n)) ∧ (∃n st q(n))

There are several questions in the same vein but these two are examples

2. Relevant equations

3. The attempt at a solution

I'm having a hard time wrapping my head around this problem. All the problems that I've worked on before are for individual values of n, I don't know how to go about proving or disproving for questions like this. I know I can prove they are equivalent by showing i) <-> ii) but I can't even tell whether the statements are equivalent or not let alone writing the proof.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Predicate logic quesion

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