I breathe when I sleep.
CONDITIONAL:
CONVERSE:
INVERSE:
CONTRA POSITIVE:
BICONDITIONAL:
Conditional: If I sleep, then I breathe.
Converse: If I breathe, then I sleep.
Inverse: If I don't sleep, then I don't breathe.
Contrapositive: If I don't breathe, then I don't sleep.
Biconditional: I breathe when I sleep if and only if I sleep when I breathe.
CONDITIONAL: If I sleep, then I breathe.
CONVERSE: If I breathe, then I sleep.
INVERSE: If I do not sleep, then I do not breathe.
CONTRAPOSITIVE: If I do not breathe, then I do not sleep.
BICONDITIONAL: I sleep if and only if I breathe.
To determine the conditional, converse, inverse, contrapositive, and biconditional of the statement "I breathe when I sleep," we'll need to understand each component.
1. Conditional Statement: A conditional statement is of the form "if P, then Q," where P represents the hypothesis or condition, and Q represents the conclusion. In this case, the conditional statement would be: "If I sleep, then I breathe."
2. Converse Statement: The converse of a conditional statement is formed by switching the hypothesis and conclusion. The converse of the given statement would be: "If I breathe, then I sleep."
3. Inverse Statement: The inverse of a conditional statement is formed by negating the hypothesis and the conclusion. The inverse of the given statement would be: "If I don't sleep, then I don't breathe."
4. Contrapositive Statement: The contrapositive of a conditional statement is formed by negating and switching both the hypothesis and conclusion. The contrapositive of the given statement would be: "If I don't breathe, then I don't sleep."
5. Biconditional Statement: A biconditional statement is formed by combining a conditional statement and its converse with the phrase "if and only if." The biconditional statement of the given statement would be: "I breathe if and only if I sleep."
It's important to note that while the original statement (conditional) and the contrapositive always have the same truth value, as do the converse and inverse, this may not be the case for the biconditional statement.