# $\lnot p$ whenever $q:\;$Do I understand this?

The phrase is not p whenever q.

I take this to mean the same thing as not p if q.

When p is false, q can be true or false.
When p is true, q is false.
When q is true, p is false.
When q is false, p can be true or false.

Stated logically, I could write this as: $q\to \lnot p$. Would that be sufficient or is there more to it?

• It is sufficient Feb 13, 2014 at 19:14

You've done just fine:

Not $p$ whenever $q$ can indeed be translated as "Not p, if q", i.e., "If q, then not p":

This tranlsates, literally, as $$q\rightarrow \lnot p$$

and note that this is equivalent to its contrapositive: $$p \rightarrow \lnot q$$

You make it yourself to complicated you are doing things double

 p | q || is "not p whenever q." true?
---|---||----------------------------
T | T ||    yes/ no (ps only one is true)
T | F ||    yes/ no (ps only one is true)
F | T ||    yes/ no (ps only one is true)
F | F ||    yes/ no (ps only one is true)


and decide line by line if the statement is true

• The first line: if p and Q are both true is "not p whenever q." true?
• second line: if p is true and Q is false is "not p whenever q." true?

and so on

GOOD LUCK