Consider the following statement form. p ∨ ~q → r ∨ q (a) The logical equivalences  p → q ≡ ~p ∨ q  and  p ↔ q ≡ (~p ∨ q) ∧ (~q ∨ p)  make it possible to rewrite the given statement form using only ~, ∧, and ∨ and not  → or ↔.  What is the result when the form is expressed without →?

Proficiency #4. [Propositional Logic] Rewrite each of the following statements using only the AND and NOT connectives. (a) PV¬Q (b) (P V Q) → R

2-Use laws and logical equivalences of propositional logic to show that ¬(p ∨ ¬(p ∧ q)) is a contradiction.

Using relational predicates ( e.g. F(s,m) for, say, s can fool m), translate the following sentences into predicate logic. You can use English words for the quantification symbols (such as For All x instead of v x) if necessary Also give the negatives of each sentence in English. a) Everybody can fool somebody b) There is no-one who can fool everyone. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

D part only plz. Thankyou.

EXERCISE 1.11.1: Valid and invalid arguments expressed in logical notation. Indicate whether the argument is valid or invalid. For valid arguments, prove that the argument is valid using a truth table. For invalid arguments, give truth values for the variables showing that the argument is not valid. (h) (1) q→p -q Ap -(p→q) 9 p -q -(p→q) Р q→P q→P P :-(p→q)