Conditional Statement

The truth table will be analyzed using the conditional statement about squares. If a figure is a square_p, thenit has four sides_q.

First Row

In the first scenario, the truth table states that the hypothesis p, a figure is a square, is true. It also states that the conclusion q, it has four sides, is also true. Therefore, it makes sense to say that p implies q.

If both hypothesis and conclusion are true, it makes sense that the conditional statement is also true.

Second Row

A true hypothesis is supposed to imply a true conclusion. In the second scenario, it is assumed that the hypothesis p is true and the conclusion q is false. Therefore, the conditional statement, p implies q, must be false. This is because a true hypothesis is followed by a false conclusion.

Third Row

The third row of the table assumes that p is false and q is true. This is saying the following statement.

This statement does not say anything about what to expect if a figure is not a square. However, this does not invalidate p implies q, as a figure might have four sides. Therefore, it is reasonable to think p implies q is still true.

In short, when the hypothesis of a conditional statement is false, the conclusion becomes irrelevant.

Fourth Row

In the last scenario, both the hypothesis and the conclusion are false. The conditional states that if a figure is not a square, then it does not have four sides. Since a figure that is not a square might not have four sides, this statement does not invalidate the conditional statement — if a figure is a square, it has four sides.

Again, a false hypothesis makes the conclusion irrelevant.