Write each of the two statements in symbolic form and determine whether they are logically equivalent. Include a truth table and a few words of explanation to show that you understand what it means for statements to be logically equivalent. Let p = “2 is a factor of n”, q = “3 is a factor of n”, and r = “6 is a factor of n”. (a) If 2 is a factor of n and 3 is a factor of n, then 6 is a factor of n. p ∨ q ∼ p∧ ∼ q → r p∧ ∼ q p ∧ q → r p ∨ q → r (b) 2 is not a factor of n or 3 is not a factor of n or 6 is a factor of n. p∨ ∼ r ∼ p∧ ∼ q → r ∼ p∨ ∼ q ∨ r ∼ p∧ ∼ q ∧ r ∼ ρ ∧ r Construct a truth table for the statements. The truth table shows that p ∧ q → r and ∼ p∨ ∼ q ∨ r have the same truth values. Therefore they logically equivalent.
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Write each of the two statements in symbolic form and determine whether they are logically equivalent. Include a truth table and a few words of explanation to show that you understand what it means for statements to be logically equivalent. Let p = “2 is a factor of n”, q = “3 is a factor of n”, and r = “6 is a factor of n”. (a) If 2 is a factor of n and 3 is a factor of n, then 6 is a factor of n. p ∨ q ∼ p∧ ∼ q → r p∧ ∼ q p ∧ q → r p ∨ q → r (b) 2 is not a factor of n or 3 is not a factor of n or 6 is a factor of n. p∨ ∼ r ∼ p∧ ∼ q → r ∼ p∨ ∼ q ∨ r ∼ p∧ ∼ q ∧ r ∼ ρ ∧ r Construct a truth table for the statements. The truth table shows that p ∧ q → r and ∼ p∨ ∼ q ∨ r have the same truth values. Therefore they logically equivalent.
