Final answer:
In a conditional statement p → q, the converse is q → p, the inverse is ¬p → ¬q, the contrapositive is ¬q → ¬p, and the biconditional is p ↔ q. The hypothesis is p. Hence, the correct answer from the options provided is d) Biconditional, contrapositive, hypothesis.
Step-by-step explanation:
For a conditional statement p → q, we can identify several related logical statements. Here are the definitions and examples of each:
- Converse: The converse of a conditional statement swaps the hypothesis and conclusion. In symbols, the converse of p → q is q → p.
- Inverse: The inverse of a conditional statement negates both the hypothesis and the conclusion. In symbols, the inverse is ¬p → ¬q (¬ represents negation).
- Contrapositive: The contrapositive negates and swaps the hypothesis and conclusion of the original statement. In symbols, the contrapositive of p → q is ¬q → ¬p.
- Biconditional: The biconditional combines the original statement and its converse, indicating that both are true. In symbols, the biconditional is p ↔ q, read as 'p if and only if q'.
- Hypothesis: This is the antecedent or the 'if' part of the conditional statement. In the statement p → q, p is the hypothesis.
To answer the student's question with the correct terminology and symbols:
- The inverse of p → q is ¬p → ¬q.
- The converse of p → q is q → p.
- The contrapositive of p → q is ¬q → ¬p.
- The biconditional is p ↔ q.
- The hypothesis is p.
- Therefore, the correct answer is d) Biconditional, contrapositive, hypothesis.