Question

P->q is false and p is true. q is a.true b.false

Answer 1

Answer:

Choice b. $q$ has to be false.

Step-by-step explanation:

Consider the truth table of $p \implies q$ ($p$ implies $q$).

• $p$ is true and $q$ is true: $p \implies q$ would be true.
• $p$ is true and $q$ is false: $p \implies q$ would be false.
• $p$ is false and $q$ is true: $p \implies q$ would be true.
• $p$ is false and $q$ is false: $p \implies q$ would also be true.

The only combination where $p \implies q$ is false is when $p$ is true and $q$ is false. Hence, the $q\!$ here must be false.