show the working out question 12 to 19

10. 11. 12. 13. 14. 15. 16. Suppose that p and q are statements so that p > q is false. Find the truth values of each of the following. a) ~P>q b) qu 0) q>p Write the converse, inverse and contrapositive of the following statements. p: It is my birthday. q: I get cake. Construct truth tables for the compound statement: a) p A (q -> ~10)- b) (~(p V 61)) -> (61 A 19)- Show using truth table that the compound statement (~p) V (q > p) is a tautology. Show using truth table that the compound statement ~(~p A q) V q is a tautology. Show using truth table that the compound statement (19 Aq) A (q > ~p) is a contradiction. Show using truth table that the compound statement (~qu)A (pA~q) is a contradiction. Show using truth table that p > q E (~p) V q. Show using truth table that ~(p V q) E (~p) A (~q). 17. Translate the following sentences, given the following statements: p t I finish writing my computer program before lunch. q : I shall play tennis in the afternoon. r 2 The sun is shining. s : The humidity is low. a) If the sun is shining, I shall play tennis this afternoon. b) Finishing the writing of my computer program before lunch is necessary for my playing tennis this afternoon. 0) Low humidity and sunshine are sufcient for me to play tennis this afternoon. 18. Express the following sentence in symbolic statement. If a student studies and does not miss a lecture, then the student does not fail. 19. Write the following sentence in symbolic form. I do not fail the course if and only if] study hard and I pass the final examination