3.4 Equivalent Statements

• Two statements are equivalent <=> if both statements have exactly the same truth values in the answer columns of the truth tables.
• Is p∧ ∼ q <=> ∼q ∨ q?
• Is ∼p ∨ ∼ q <=> ∼(p ∨ q)?
• The last is a special case of De Morgan's Laws
  • ∼(p ∧ q) <=> ∼p ∨ ∼ q
  • ∼(p ∨ q) <=> ∼p ∧ ∼ q
• In some sense, change the and to or, and negate every item.
• We also need to note ∼(∼p) <=> p
• 9 Through 18 page 147, especially 15 and 16.
• We are also told that p → q <=> ∼p ∨ q (conditional)
• The following is equivalent to the conditional.
  • ∼ q → ∼ p contrapositive of the conditional
• And the following are equivalent
  • q → p (converse of conditional)
  • ∼ p → ∼ q Inverse of the conditional
• Look at 19-30
• Look at 31 - 38
• 39-60