Chapter 2 Section 2: Conditional Statements

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Questions and Answers

What is a conditional statement?

  • If p then q (correct)
  • If p and not q
  • If q then p
  • If not q then not p

What is the negation of a conditional statement?

p and not q

What is the contrapositive of the statement 'If p then q'?

  • If ~p then q
  • If ∼p then ∼q
  • If q then p
  • If ∼q then ∼p (correct)

What is the converse of the statement 'If p then q'?

<p>If q then p</p> Signup and view all the answers

What is the inverse of the statement 'If p then q'?

<p>If ~p then ~q</p> Signup and view all the answers

What does 'p only if q' mean?

<p>If not q then not p</p> Signup and view all the answers

What is a biconditional statement?

<p>p if, and only if, q (D)</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Conditional = If p then q Negation of a Conditional = p and not q Contrapositive = If ∼q then ∼p Converse = If q then p Inverse = If ~p then ~q Biconditional = p if, and only if, q Only If = If not q then not p Order of Operations = 1. negations, 2. ands, ors, 3. conditionals</p> Signup and view all the answers

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Study Notes

Conditional Statements

  • A conditional statement is expressed as "If p then q" or "p implies q," denoted as p → q.
  • The truth value of a conditional is false only when p is true and q is false; it is true in all other scenarios.
  • In a conditional, p is known as the hypothesis or antecedent, while q is the conclusion or consequent.

Negation of a Conditional

  • The negation of "if p then q" is equivalent to "p and not q," indicating when the original statement is not true.

Contrapositive

  • The contrapositive of a conditional statement "If p then q" is written as "If not q then not p," symbolically represented as ∼q → ∼p.
  • The contrapositive logically carries the same truth value as the original conditional statement.

Converse

  • The converse of a statement "if p then q" is formed by reversing the order to "if q then p."

Inverse

  • The inverse of the statement "if p then q" is created by negating both parts, resulting in "if not p then not q."

Only If

  • The phrase "p only if q" is logically interpreted as "if not q then not p," which is also equivalent to "if p then q."

Biconditional

  • A biconditional statement is expressed as "p if and only if q," denoted as p ↔ q.
  • It is deemed true when both p and q possess the same truth values and false if they differ.

Order of Operations

  • The hierarchy for evaluating logical expressions follows this order:
    • Negations have the highest priority.
    • Followed by conjunctions (ands) and disjunctions (ors).
    • Conditionals come last in the order of operations.

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