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.