MAT125- Discrete Mathematics Section 2.1 and 2.2 NAME SHOW ALL WORK FOR ALL PROBLEMS ALWAYS. USE EXTRA SHEETS IF NEEDED. DO NOT SKIP STEPS. I CANNOT READ mental calculations…so SHOW ALL STEPS! Show T F F? ? or F F F? ? versus just an answer of F! 1. Use truth tables to find the truth values of the statements, as given. State whether the statements below are tautologies or contradictions or neither with a written reason to justify your answer. Show all intermediate steps for calculating the truth values. I do NOT want only answers. (a) ~(p ?~ )q ? (q? ~ p) (b) ( p?~ )q ? ~ p 2. (a) Translate the statement “If this is how things are gonna be and I’m not gonna do the book HW problems, then am not gonna get a C!” into logical symbols. Then construct the truth table for the compound statement. To help do this, define the simple statements (as we always do)… t: This is how things are gonna be h: I’m gonna do the book HW problems c: I will get a C 2(b). Use truth tables to show which, if any, of the two statements below are logically equivalent to the given statement above. Show all work. Do not skip steps! Clearly state whether the statements (using logical symbols) are logically equivalent and why. If there are no logical equivalences, clearly say so symbolicallly, with a reason. (a) ~ r? (~ p?~ q) (b) (p? q) ? r Document Preview:

MAT125- Discrete Mathematics Section 2.1 and 2.2 NAME SHOW ALL WORK FOR ALL PROBLEMS ALWAYS. USE EXTRA SHEETS IF NEEDED. DO NOT SKIP STEPS. I CANNOT READ mental calculations…so SHOW ALL STEPS! Show T F F? ? or F F F? ? versus just an answer of F! 1. Use truth tables to find the truth values of the statements, as given. State whether the statements below are tautologies or contradictions or neither with a written reason to justify your answer. Show all intermediate steps for calculating the truth values. I do NOT want only answers. ~(p ?~ )q ? (q? ~ p) ( p?~ )q ? ~ p 2. (a) Translate the statement “If this is how things are gonna be and I’m not gonna do the book HW problems, then am not gonna get a C!” into logical symbols. Then construct the truth table for the compound statement. To help do this, define the simple statements (as we always do)… t: This is how things are gonna be h: I’m gonna do the book HW problems c: I will get a C 2(b). Use truth tables to show which, if any, of the two statements below are logically equivalent to the given statement above. Show all work. Do not skip steps! Clearly state whether the statements (using logical symbols) are logically equivalent and why. If there are no logical equivalences, clearly say so symbolicallly, with a reason. (a) ~ r? (~ p?~ q) (b) (p? q) ?r

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