If p∨q is true, then what must be true about the truth values of p and q?
if you mean P and Q is true, then P and Q are both true.
I believe p^q is p and q
pvq would be p or q. In that case, either one or both must be true.
To determine what must be true about the truth values of p and q when p∨q is true, we can look at the truth table for the logical operator "∨" (logical OR).
The truth table for ∨ is as follows:
p | q | p∨q
------------------
T | T | T
T | F | T
F | T | T
F | F | F
Here, T represents "true" and F represents "false".
According to the truth table, the statement p∨q is true in the first three rows. This means that at least one of p or q must be true in order for p∨q to be true.
So, when p∨q is true, either p is true, or q is true, or both p and q are true. It is not necessary for both p and q to be true to satisfy the condition.