(8 marks) Use logical equivalences from the Logical Equivalences handout to verify the fol- lowing claims. Supply a reason for each step. Use only one law at each step. Be explicit about each law that you use, including the double negative and commutative laws 2. 3. (8 marks) For each of the following statement forms, give a logically equivalent statement form that contains only statement variables, parentheses, and the connectives and ~. Justify your answers with truth tables a) C (b) pV q (c) pAq 4. (16 marks) Let the statement S be defined as follows, where n is some particular number under discussion: S: "If n is prime, then n is odd or n is equal to 2." Assuming that S is true1, which of the following must also be true? Justify your answers Use the words converse, inverse, contrapositive, and negation when possible. (a) If n is odd or n is equal to 2, then n is prime (b) If n is neither odd nor equal to 2, then n is not prime (c) n is prime only if it is odd or equal to 2 n is not prime unless it is odd or equal to 2. (e) If n is not prime, then it is neither odd nor equal to 2. (f) n is prime and neither odd nor equal to 2. (g) A necessary condition for n to be prime is that it is odd or equal to 2. (h) A sufficient condition for n to be prime is that it is odd or equal to 2. Actually, S is true no matter what number is being discussed