Truth Tables, Implications, Contrapositives and Converses

(a) Use truth tables to prove that an implication is always equivalent to its contrapositive. Site an example where this is so. (b) Use truth tables to prove that an implication may not be equivalent to its converse. Site an example where this is so.

Logical Equivalents

Determine whether (p --> q ) / (p --> r) and p --> (q / r) are logically equivalent. Show all work.

Basic Proof

Prove or disprove the following: If the integer n is divisible by 3, then (nxn) is divisible by 3. Show work.

Integer Proofs by Contradiction

Assume that n is a positive integer. Use the proof by contradiction method to prove: (a) If 7n + 4 is an even integer, then n is an even integer. (b) Prove: n is an even integer iff 7n + 4 is an even integer. (Note this is an if and only if (iff) statement.

Set Operations : Subtraction, Cartesian Products, Direct Sums and Intersection

Let A = {1,3,5} and B = {3,5}. Compute: (a) A - B (b) A X B (c) A (plus sign with a circle around it) B (d) A ∩ (B - A)