Answer to Question #26098 in Discrete Mathematics for Venzo

Question

Consider the following statement:

M = Syahmi will get grade A for his mathematic subject if and only if he study the subject every day.

(i) Write each statement in terms of p and q. Then re-write the statement into logical notation.

(ii) State the negation, converse and contrapositive of the above statement, M, in symbolic form.

(iii) Using the answer in (i), determine the truth table of the propositions in statement M.

(iv) Is the statement M a tautology, contradiction or neither? Justify your answer.

(v) Construct a truth table for r ˅ q --> (ṝ ᴧ p) and p ᴧ q ↔ r. Determine whether both proposition is logically equivalent. Justify your answer.