Answer:
Choice b. [tex]q[/tex] has to be false.
Step-by-step explanation:
Consider the truth table of [tex]p \implies q[/tex] ([tex]p[/tex] implies [tex]q[/tex]).
- [tex]p[/tex] is true and [tex]q[/tex] is true: [tex]p \implies q[/tex] would be true.
- [tex]p[/tex] is true and [tex]q[/tex] is false: [tex]p \implies q[/tex] would be false.
- [tex]p[/tex] is false and [tex]q[/tex] is true: [tex]p \implies q[/tex] would be true.
- [tex]p[/tex] is false and [tex]q[/tex] is false: [tex]p \implies q[/tex] would also be true.
The only combination where [tex]p \implies q[/tex] is false is when [tex]p[/tex] is true and [tex]q[/tex] is false. Hence, the [tex]q\![/tex] here must be false.
