Answer:
The truth values of p q is equivalent to (p q) (q p).
Explanation:
n conditional statements, "If p then q" is denoted symbolically by "p q"; p is called the hypothesis and q is called the conclusion. For instance, consider the two following statements:
If Sally passes the exam, then she will get the job.
If 144 is divisible by 12, 144 is divisible by 3.
Let p stand for the statements "Sally passes the exam" and "144 is divisible by 12".
Let q stand for the statements "Sally will get the job" and "144 is divisible by 3".
The hypothesis in the first statement is "144 is divisible by 12", and the conclusion is "144 is divisible by 3".
The second statement states that Sally will get the job if a certain condition (passing the exam) is met; it says nothing about what will happen if the condition is not met. If the condition is not met, the truth of the conclusion cannot be determined; the conditional statement is therefore considered to be vacuously true, or true by default.