The second statement is the of the first

The second statement is the of the first. a= b 33 7b contrapositive contradiction inverse converse

The Correct Answer and Explanation is:

The correct answer is: C. inverse

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Explanation:

The first statement given is:

• a⇒ba \Rightarrow b

This is a conditional statement, meaning if a is true, then b is also true.

The second statement is:

• ¬a⇒¬b\neg a \Rightarrow \neg b

This reads as if not a, then not b.

This type of transformation is called the inverse of a conditional statement.

Let’s break down the four terms to understand why:

1. Original Statement (Conditional):
   a⇒ba \Rightarrow b
   “If a, then b.”
2. Inverse:
   ¬a⇒¬b\neg a \Rightarrow \neg b
   This negates both the hypothesis and the conclusion of the original.
   “If not a, then not b.”
   → This matches the second statement, so this is the correct answer.
3. Converse:
   b⇒ab \Rightarrow a
   This switches the hypothesis and conclusion without negating them.
   “If b, then a.”
4. Contrapositive:
   ¬b⇒¬a\neg b \Rightarrow \neg a
   This switches and negates both the hypothesis and conclusion.
   “If not b, then not a.”
5. Contradiction:
   A contradiction is a logical inconsistency, such as a statement that is always false (e.g., a∧¬aa \wedge \neg a).
   → This is not what’s happening here.

Summary:

• The inverse of a statement a⇒ba \Rightarrow b is ¬a⇒¬b\neg a \Rightarrow \neg b.
• This does not mean it is logically equivalent to the original statement (only the contrapositive is logically equivalent).
• Therefore, the second statement is the inverse of the first.

✅ Correct answer: C. inverse