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Concept

Conditional Statement

A conditional statement combines two statements: a hypothesis and a conclusion A conditional statement can be written in if-then form.
The hypothesis of a conditional statement comes after the word if, and the conclusion comes after the word then. The symbolic representation can also be read as implies
By using a truth table for a conditional statement, the conditions under which the statement is true can be determined. The truth table below shows the truth values for hypothesis and conclusion
Conditional Statement
T T T
T F F
F T T
F F T

A conditional statement is false only when the hypothesis is true and the conclusion false. In any other case, a conditional statement is true.

Why

Analyzing the Truth Values of Conditional Statements
The truth table will be analyzed using the conditional statement about squares.

First Row

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

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 is true and the conclusion is false. Therefore, the conditional statement, implies 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 is false and 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 implies as a figure might have four sides. Therefore, it is reasonable to think implies 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.

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