Question

If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by q p?

Answer 1

Answer with Explanation

In 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 John passes the exam, then she will get the job.
• If 225 is divisible by 15, 225 is divisible by 5.
• Let p stand for the statements "John passes the exam" and "225 is divisible by 15".
• Let q stand for the statements "John will get the job" and "225 is divisible by 5".

The hypothesis in the first statement is "225 is divisible by 15", and the conclusion is "225 is divisible by 5". The second statement states that John 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.