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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