I am trying to figure out if this statement is true or false. It says:
“If I do not get my car fixed, I will miss my job interview,” says Jack. Later, you come to know that Jack’s car was repaired but that he missed his job interview. Was Jack’s statement true or false? Explain.
From looking at a truth table, statement A (The car not being fixed) is false. This is because his hypothesis of the car not being fixed (what we assume is to be true), was later contradicted, even though the statement B (Missing the interview) was still true.
Is this reasoning correct? Or am I wrong?
The statement $P \implies Q$ is false when $P$ is true and $Q$ is false. Here your statement $A$ is false and $B$ is true, so $A \implies B$ is still true by definition.