Note: Do not use it is not the case /true that (1) Let p: "Anna ate the apple, q: "Anna ate the orange", r: "The apple is in the basket" 8: "The orange is in the basket". Answer the following (a) Write the converse in symbolic for : Anna ate the apple and did not eat the orange unless Both the apple and the Orange are in the basket. (b) Write the contrapositive in English using whenever for: Neither the apple nor the orange in the basket is sufficient for that Anna ate either the apple or the orange (c) Write the negation in English for part (b) (2) Let P(x,y):"a is friend of y". Q(x): "x is funny, R(x) : "r is smart" and M(x):"r is talkative". The domain is UOB students. Answer the following: (a) Write the symbolic for : All funny students are not friends of all smart students. (b) Write the English for : Vx: -Q(x) R(x) +-P(Karim, x) (e) Write the symbolic : Some talkative students are friends of all not talkative students (d) Write the negation in Symbolic starting with Vx, By: There is a funny non talkative student who is friend of all UOB students. (3) Determine the truth-values of the following. Give reasons. (a) Vx3y : x + y = 1 for x, y ez (b) Vxy e R+ : Vary (e) 3x E ZVEZ:+ y = 1