Geometry

Question Analysis:
This question tests the understanding of logical equivalence in conditional statements.
The main focus is on identifying which of the given options is logically equivalent to p→q.

Key Concept Explanation:
The contrapositive of a conditional statement p→q is logically equivalent to the original statement.
The contrapositive is formed by negating and swapping the hypothesis and conclusion, resulting in ∼q→∼p.

Step-by-Step Solution:
Original statement: p→q
Hypothesis (p): "If p is true."
Conclusion (q): "Then q is true."
Contrapositive: Negate and swap the hypothesis and conclusion.
New hypothesis (∼q): "If q is not true."
New conclusion (∼p): "Then p is not true."
Symbolic representation of the contrapositive: ∼q→∼p.
The contrapositive is logically equivalent to the original statement p→q.
The correct answer is C.

Option Analysis:
A) q→p
This represents the converse of the statement, which is not logically equivalent to p→q.
B) ∼p→∼q
This represents the inverse of the statement, which is not logically equivalent to p→q.
C) ∼q→∼p
This is the...