MadeEasy Test Series Mathematical Logic - Propositional Logic

Question

Consider two well-formed formula in proposition logic:

Which of the following is correct?

1. F1 is satisfiable, F2 is valid
2. F1 is unsatisfiable, F1 is satisfiable
3. F1 is unsatisfiable, F2 is valid
4. F1 and F2 both are unsatisfiable

Comments

Why can't we solve by resolution principle by which if we combine first two MAX terms of POS, result is empty and hence unsatisfiable?

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b?

What is difference between satisfiable and valid?

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satisfiable means some true and some false

valid  means  all true.

Answer 1

Let's see F1 :-

(p<->q)^(~p<->q) this is unsatisfiable , since it will be satisfiable only if both are true .

p<->q is true in only two cases TT and FF .

And in both the cases the other term will be False , so it is unsatisfiable.

Now the other one  :-

(p+~q)(~p+q)(~p+~q) = (pq+~q~p)(~p+~q) = ~p~q which is satisfiable.