if a conditional and its converse are always true then the statement is a
If a conditional statement and its converse are always true, then the statement is a biconditional (or if and only if) statement.
If a conditional statement and its converse are always true, then the statement is a biconditional statement.
To understand this, let's first define what a conditional statement and a converse are:
- Conditional statement: This is an "if-then" statement of the form "If P, then Q". The condition (P) represents the hypothesis or the antecedent, and the result (Q) represents the conclusion or the consequent.
- Converse: The converse of a conditional statement is formed by switching the hypothesis and the conclusion. So, it takes the form "If Q, then P".
Now, if a conditional statement and its converse are always true, it means that both the original statement and its converse are always true. This suggests that the hypothesis and conclusion are equivalent, meaning that "P if and only if Q" or "P ↔ Q".
This is known as a biconditional statement, which expresses that both conditions P and Q always hold true together. In other words, if P is true, then Q must also be true, and conversely, if Q is true, then P must also be true.
In summary, if a conditional statement and its converse are always true, it implies a biconditional statement where both the hypothesis and conclusion are equivalent.