Question

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

Answer 1

Choice b.
`q` has to be false.

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.