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Concept

$Words:Symbols: Ifp,thenq.p⇒q $

if,and the conclusion comes after the word

then.The symbolic representation can also be read as

$p$ implies $q.$

$Ifhypothesispa figure is a square ,thenconclusionqit has four sides . $

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 $p$ and conclusion $q.$ Conditional Statement | ||
---|---|---|

$p$ | $q$ | $p⇒q$ |

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.

The truth table will be analyzed using the conditional statement about squares.
## First Row

## Second Row

## Third Row

## Fourth Row

$Ifpa figure is a square ,thenqit has four sides . $

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.

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.

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.

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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