(2)3. Apply a series of logical equivalences and/or rules of inference to show that rg follows from the following premises. Be sure to indicate the line mumber(s) and logical equivalence or rule of inference used in each step.

Determine whether (p→g) ^(-p Vr) and p V (q^r) are two logically equivalent propositions.

38. Which of the following are well formed symbolic propositional statements? i. - [p → (q ^ p)] ii. - [p - (q → p)] iii. (p ^ -q) v (q → -p) A. i and ii only B. ii and iii only C. i and iii only D. i, ii and ii NTIA EDIFICA

Justify why these premises lead to conclude E.

help me

3. Consider the following propositions: P→ 9, g^-p. -P→→q, -pv q, 9 → P. -q V p, q→P. р^-4. (a) Which proposition is the converse of p → q? (b) Which proposition is the contrapositive of pq? (c) Which propositions are logically equivalent to P→q?

(a) Let P, Q and R be simple statements. Use only ONE suitable method throughout to determine precisely whether the following compound statement is a tautology, contradiction or contingent statement: R= [(P ^ Q) → (P V ~R)] (b) Express the following using predicates statements with the least number of words: (i) The sum of the square of any three integer is even. (ii) All Covid-19’s Vaccines do not work on any Covid-19's variants.

Q.5) Use a truth table to determine whether the argument is valid or invalid. а. p ->~q b. (~p v q) ^ (~p ->q)

(6) Use a truth table to determine whether (p^ (qVr)) and ((p^q) V (p^r)) are logically equivalent.

1. Determine the rule of inference used in the following arguments. А. а — (b лс) (ьле) —>d .'.a d В. jak ::(jAk)V(IAm) ~(r^s)→~(pVs) C. :(rAs)→[~(r^s)^~(pVs)]