We know that, if p is true, q is true. However, what if p is false? We would have no information whatsoever as to the truth of falsehood of q.
Take the following example.
If it is snowing, it is cold outside. (If p, then q.)
It is not snowing. (Not p.)
Do we know if it's cold outside from the above information? Of course not. While the occurrence of snowfall suggests cold weather, there are many cold days in which no snow is to be found. Thus, we do not know if it is cold or not just by knowing that it is not snowing.
Therefore, q may be either true or false in instances where not-p is the case.
Answers & Comments
Verified answer
That is true.
We know that, if p is true, q is true. However, what if p is false? We would have no information whatsoever as to the truth of falsehood of q.
Take the following example.
If it is snowing, it is cold outside. (If p, then q.)
It is not snowing. (Not p.)
Do we know if it's cold outside from the above information? Of course not. While the occurrence of snowfall suggests cold weather, there are many cold days in which no snow is to be found. Thus, we do not know if it is cold or not just by knowing that it is not snowing.
Therefore, q may be either true or false in instances where not-p is the case.
I hope this helps.
That statement is true.
If P then Q
P= You're in Los Angeles
Q= You're in California
If you're in Los Angeles then you're in California. <<True statement>>>
You are not in Los Angeles <<<<P is false>>>>
Then you may or may not be in California "Q may be either true or false"
false