Questions: (1) Let p and q be the propositions p: It is below freezing. q: It is snowing. Write these propositions using p and q and logical connectives (including negations). a) It is below freezing and snowing b) It is below freezing but not snowing c) It is not below freezing and it is not snowing d) It is either snowing or below freezing (or both) e) If it is below freezing, it is also snowing f) Either it is below freezing or it is snowing, but it is not snowing if it is below freezing g) That it is below freezing is necessary and sufficient for it to be snowing (2) Show that each of these conditional statements is a tautology and are logically Equivalent by using truth tables (pq) p p (p V q)=(p^q) (pq) =(pa) (3) Express the sentence using predicate logic (2 mark) (a) Some students are smart (b) Ali take project if and only if he take summer training (c) Ali is student (d) All students loves ali (4) If x, y are integers and x and y are both odd, then x +y is even. Proof this by the Direct Proof. (5) Give a proof by contradiction of theorem "If n + 1 is odd, then n is even" (6) Prove by exhaustion that p = n + 2 is not a multiple of 4, where n is an integer, 2