High School

Correctly match the p-q notation with the corresponding related conditional statements.

A. \( pq \): Conditional, \( qp \): Converse, \( -p-q \): Inverse, \( -q-p \): Contrapositive
B. \( pq \): Conditional, \( q \rightarrow p \): Converse, \( -p-q \): Contrapositive, \( -q-p \): Inverse
C. \( pq \): Conditional, \( qp \): Contrapositive, \( -p-q \): Inverse, \( -q-p \): Converse
D. \( pq \): Conditional, \( qp \): Inverse, \( pq \): Converse, \( qp \): Contrapositive

Answer :

Final answer:

The proper matching of the p-q notation with conditional statements is Option B: pq as Conditional, q→p as Converse, ¬p→¬q as Contrapositive, and ¬q→p as Inverse.

Explanation:

The correct matching of p-q notation with the corresponding related conditional statements is as follows:

  1. p→q: This is the Conditional statement. It means 'if p, then q'.
  2. q→p: This is the Converse of the conditional. It reverses the hypothesis and the conclusion, meaning 'if q, then p'.
  3. ¬p→¬q: This is the Inverse of the conditional. It negates both the hypothesis and the conclusion, meaning 'if not p, then not q'.
  4. ¬q→¬p: This is the Contrapositive of the conditional. It negates and reverses the hypothesis and conclusion, meaning 'if not q, then not p'.

Using these definitions, we can analyze the provided options. The correct answer is Option B which pairs each statement accurately:

  • pq: Conditional
  • q→p: Converse
  • ¬p→¬q: Contrapositive
  • ¬q→p: Inverse

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