A bi-conditional statement is a logical statement that combines a conditional statement and its converse using the phrase "if and only if" (often abbreviated as "iff"). It indicates that both the original condition and its converse are true.

The structure of a bi-conditional statement is:

• "p if and only if q," which can be written as $p \iff q$.

This means that:

• If $p$ is true, then $q$ must also be true.
• If $q$ is true, then $p$ must also be true.

In other words, both statements $p \rightarrow q$ (if $p$, then $q$) and $q \rightarrow p$ (if $q$, then $p$) must be true for a bi-conditional statement to hold.

Example:

"If two angles are supplementary, then the sum of their measures is 180 degrees" and its converse, "If the sum of the angles is 180 degrees, then the angles are supplementary," together form the bi-conditional statement:

• "Two angles are supplementary if and only if the sum of their measures is 180 degrees."

Thus, the definition you gave:

• "The conjunction of a conditional statement and its converse statement" is correct.

Would you like more details or clarification on this?

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Here are 5 related questions for further exploration:

1. What is the difference between a conditional and bi-conditional statement?
2. How do you negate a bi-conditional statement?
3. Can a bi-conditional statement be true if one part is false?
4. How does the truth table of a bi-conditional differ from that of a conditional?
5. How would you express a bi-conditional statement in terms of set theory?

Tip: The symbol $\iff$ is used in logic to represent a bi-conditional statement and ensures that both directions (if and only if) are considered.