# Discrete Mathematics home work 5 questions

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Discrete Mathematics (MAT 214) Homework 1 Complete the following problems on a separate sheet of paper. Write as much as possible for full credit, including calculator work. This assignment is due on Wednesday, January 23rd . 1) Write a truth table for the following: a) ∼(p ∧ q) ∨ (p ∨ q) b) p ∧ (q ∨ ∼r) 2) Determine whether the statement forms are logically equivalent. Do this by constructing a truth table and include a sentence that justifies your answer. a) p ∧ t and p b) (p ∧ q) ∨ r and p ∧ (q ∨ r) 3) Using De Morgan’s Laws, write the negation of the following statement. a) −10 < x < 2 b) x ≤ −1 or x > 1 4) Using the list of logical equivalences given out to verify the following logical equivalences. Supply a reason for each step. a) ∼(p ∨ ∼q) ∨ (∼p ∧ ∼q) ≡ ∼p b) (p ∧ (∼(∼p ∨ q))) ∨ (p ∧ q) ≡ p 5) Are the following statement forms tautologies, contradictions, or neither? Use truth tables to support your answer. a) ((∼p ∨ q) ∨ (q ∨ r)) ∨ ∼q b) (∼p ∨ q) ∨ (p ∧ ∼q) c) (p ∧ q) ⊕ (q ∧ p)

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Tutor went the extra mile to help me with this essay. Citations were a bit shaky but I appreciated how well he handled APA styles and how ok he was to change them even though I didnt specify. Got a B+ which is believable and acceptable.

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