Question

9. Let Pland P2 denote the following propositions: P1="CS is difficult or not many students like CS“, P2="If math is easy, then CS is not difficulty". Suppose that both Piand P2 are true, determine if the following proposition is always) true. Prove your answer. “Math is not easy if many students like CS",

Answer 1

O using derivation : Let: a : cs is difficult bi Student like is ci maths is easy .. then P1 = a vnb. - P2 = ( Na 1. avab 2. ¿ Ana 3. wbra [ commutativity on 1] 4 b7 a [ Using Implication on 3] :5. b. [ Assume from 4] 6. [ Applying modus ponens on 4 & 5] 7.00 [ Applying modus tollens. on 2&6 8. b twc ( conditional proof on 584) It means b Inc is true ie Math is not easy if many students like CS I

Modus ponens: If p q is true and p is. true, therefore q must be true. Modus Tollens : If Pyq is true and q is I false, therefore p must be false. © By Truth table:

I a b c wawb wc aumb (twabing E T T T F F F T F É T T F F F T IT TT T F T F T F T FT IT E F F T T T PT. F TTT . E FUT IF I F T F T F ; FT T Е Е Ет т т E (Т ТЕТ E F F FT T T IT TJ-T To t ttt Given Pi and P2 are true therefore A E a I Mathis not easy if many students like is is also true. above the respective column of ... btuC is true when aurb & ctwa is true.