Question

Here is a truth table for three mystery compound propositions Pi, P2, and P3, each consisting of the propositional variables w, x, y, 2. 1 2 13 TTTFT TF TTFTTFT TTFFTFF TFF T TFF FTFTTT FT FF FF F FF TFTTF FFFTFFT FFFFTFT ts) a. Is (R Λ P ) → P a tautology? If so, explain. If not, give all counterexamples ts) b. Is P → (R v PJ ) a contradiction? If so, explain. If not, give all counterexamples

Answer 1

(a) gs(P_1 intersection p_2) rightarrow a tautology ? By the given table on question we will see the new truth table (By question pick all possible p_1 p_1 and p_3) By the truth tables we can say its not a tautology Because for tautology all {(p_1 intersectionp_2) rightarrow p_3} must be 'T'. But we can see p_1 intersection p_2 is true But p_3 is not true so conclusion is false hence it ie not a tautology gt angle (p_3 rightarrow(p_1 union p_2) a contradiction ? if so, explain, if not give all the sample By the given table we will pick all be possibility of p_1, p_2 and p_3 and make the truth table Now, By the table we can say it's not a contradiction Because there is a truth on conclusion of (rightarrow p_3 rightarrow (p_1 v p_2)) Thus it is not a contradiction Because p_2 rightarrow Truth and (p_1 v p_2) rightarrow false