Try making up two of your own conditional statements with a false hypothesis and explain why they must be true.

Another example you can use is P:trees provide air, Q: 7 is an odd number. Write pq as a sentence. Then construct a truth table for this conditional. Solution: The conditional pq represents " If trees provide air, then 7 is an odd number." Trees provide air is the hypothesis, and 7 is an odd number is the conclusion. Note that the logical meaning of this conditional statement is not the same as its intuitive meaning. In logic, the conditional is defined to be true unless a true hypothesis leads to a false conclusion.

The implication of pq is that: since trees provide air, this makes 7 an odd number. However, intuitively, we know that this is false because the trees and the number 7have nothing to do with one another! Therefore, the logical conditional allows implications to be true even when the hypothesis and the conclusion have no logical connection