If `p to q` is an implication, then the implication `~q to ~p` is called its:
(A) Converse
(B) Contrapositive
(C) Inverse
(D) Alternative

Options

A. Converse
B. Contrapositive
C. Inverse
D. Alternative

Answer

To solve the question, we need to analyze the implications and their relationships. Let's break it down step by step.

### Step 1: Understand the implication
We start with the implication \( p \to q \), which means "if \( p \) is true, then \( q \) is also true."

**Hint:** Remember that an implication consists of a hypothesis (antecedent) and a conclusion (consequent).

### Step 2: Identify the contrapositive
The contrapositive of an implication \( p \to q \) is formed by negating both the hypothesis and the conclusion and then reversing them. Thus, the contrapositive of \( p \to q \) is \( \neg q \to \neg p \).

**Hint:** The contrapositive is always logically equivalent to the original implication.

### Step 3: Analyze the options
Now we look at the options provided:
- (A) Converse: This would be \( q \to p \).
- (B) Contrapositive: This is \( \neg q \to \neg p \).
- (C) Inverse: This would be \( \neg p \to \neg q \).
- (D) Alternative: This is not a standard term related to implications.

**Hint:** Make sure to match the definitions of each term with the corresponding logical statements.

### Step 4: Conclusion
Since we have identified that the implication \( \neg q \to \neg p \) corresponds to the contrapositive of the original implication \( p \to q \), the correct answer is:

**Answer:** (B) Contrapositive