Question

Let p: The kitchen is clean.
Let q: The bedroom is clean.

Which statement is true if the kitchen is clean but the bedroom is not clean?

If p is true, then q is true.
Statement q is true if and only if p is true.
Both p and q are true.
Statement p or q is true.

Answer 1

Given that \( p \): "The kitchen is clean" is true and \( q \): "The bedroom is clean" is false, we can evaluate the provided statements:

1. **If p is true, then q is true.**
This statement is false because \( p \) is true (the kitchen is clean) and \( q \) is false (the bedroom is not clean).

2. **Statement q is true if and only if p is true.**
This statement is also false because it asserts that \( q \) (the bedroom is clean) is true only if \( p \) (the kitchen is clean) is true. Since \( q \) is false and \( p \) is true, the biconditional is not satisfied.

3. **Both p and q are true.**
This statement is false because while \( p \) is true, \( q \) is false.

4. **Statement p or q is true.**
This statement is true because \( p \) is true (the kitchen is clean), so the "or" statement as a whole is true regardless of the truth value of \( q \).

Therefore, the only true statement given that the kitchen is clean but the bedroom is not clean is **Statement p or q is true.**