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The question asks for the equivalent conditional of the given statement \( a \implies b \). To solve this, we need to understand the rules of logic for conditional statements.

The equivalent conditional of \( a \implies b \) is its contrapositive, which is \( \neg b \implies \neg a \). This means "if not \( b \), then not \( a \)" is logically equivalent to "if \( a \), then \( b \)".

Now, let's analyze the choices:
1. \( a \implies \neg b \) – This is not correct, as it's a negation of the conclusion.
2. \( \neg b \implies \neg a \) – This is correct, as it represents the contrapositive.
3. \( \neg a \implies \neg b \) – This is not correct, as it switches the roles of the variables incorrectly.
4. \( b \implies a \) – This is the converse of the original statement, not the contrapositive.

Therefore, the correct answer is **\( \neg b \implies \neg a \)**, which corresponds to the second option.

Would you like more details or have any questions?

Here are 5 related questions to think about:
1. What is the converse of a conditional statement?
2. What is the inverse of a conditional statement?
3. Can a conditional statement be logically equivalent to its converse?
4. How does a biconditional statement differ from a regular conditional?
5. What are other examples of logically equivalent statements?

**Tip**: Always remember that the contrapositive of a conditional statement is logically equivalent to the original conditional statement.

Given the conditional a implies b, what is the equivalent conditional?

Understand how to find the equivalent conditional of the statement a implies b. The contrapositive ¬b implies ¬a is logically equivalent to the original statement. This question covers key concepts in logic and conditionals, suitable for advanced high school or college students.

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