## Why is conditional true when antecedent is false?

When the antecedent is false, **the truth value of the consequent does not matter**; the conditional will always be true. A conditional is considered false when the antecedent is true and the consequent is false.

Conditional.

P | Q | P ⇒ Q |
---|---|---|

F | F | T |

## What happens if the condition in a conditional is false?

A conditional statement is false if hypothesis is true and **the conclusion is false**. The example above would be false if it said “if you get good grades then you will not get into a good college”. If we re-arrange a conditional statement or change parts of it then we have what is called a related conditional.

## What is an example of a false conditional statement?

False: **If a person is 14 years old, then the person is a freshman.** **I do not eat meat on religious grounds.** “This is a false conditional sentence because the condition expressed in the conditional clause is known to the speaker to have already been fulfilled or realized.” They are all false conditionals.

## What is the antecedent of a conditional?

1Conditional, Antecedent, Consequent. For propositions P and Q, the conditional sentence P⟹Q P ⟹ Q is the proposition “If P, then Q. ” **The proposition P** is called the antecedent, Q the consequent. The conditional sentence P⟹Q P ⟹ Q is true if and only if P is false or Q is true.

## When a statement is true Its _ is false and when a statement is false Its _ is true?

This is usually referred to as “negating” a statement. One thing to keep in mind is that **if a statement is true, then its negation is false** (and if a statement is false, then its negation is true). Let’s take a look at some of the most common negations.

## Is it possible to have a series of true conditional statements that lead to a false conclusion?

In logic, **the conditional is defined to be true unless a true hypothesis leads to a false conclusion**. The implication of a b is that: since the sun is made of gas, this makes 3 a prime number.

Definition: A Conditional Statement is…

p | q | p q |
---|---|---|

F | F | T |

## Is true in all cases except when the antecedent is true and the consequent is false?

The “⊃” symbol is called the “horseshoe” and it represents what is called the “material conditional.” **A material conditional** is defined as being true in every case except when the antecedent is true and the consequent is false.

## What is the truth value of a given implication if the antecedent is false and the consequent is true?

If the antecedent (P) is true and the consequent (Q) is false, then the implication **does not hold (true)**. That is, a true antecedent cannot imply a false consequent: truth cannot imply falsity.

## Is the value considered true or false in a conditional?

The truth value of a conditional statement **can either be true or false**. In order to show that a conditional is true, just show that every time the hypothesis is true, the conclusion is also true.

## Can a conditional be true if the consequent is false?

A conditional asserts that if its antecedent is true, its consequent is also true; **any conditional with a true antecedent and a false consequent must be false**. For any other combination of true and false antecedents and consequents, the conditional statement is true.

## How do you know if a math statement is true or false?

**A false statement is one that is not correct**. For example, the number 3 is not equal to 4, so a statement that says that 3 and 4 are equal would be false. Three is not equal to 6 divided by 3, so 3 = 6 / 3 would also be a false statement.

## What is the truth value of the conditional statement when the hypothesis is false?

The conditional statement P→Q means that Q is true whenever P is true. It says **nothing about the truth value of Q when P is false**. Using this as a guide, we define the conditional statement P→Q to be false only when P is true and Q is false, that is, only when the hypothesis is true and the conclusion is false.

## What is a conditional statement that is false but has a true inverse?

Negating both the hypothesis and conclusion of a conditional statement. For example, the inverse of “If it is raining then the grass is wet” is “If it is not raining then the grass is not wet”. Note: As in the example, **a proposition** may be true but its inverse may be false.

## What is the truth value of the conditional statement when the hypothesis is true and the conclusion is false *?

Though it is clear that a conditional statement is false only when the hypothesis is true and the conclusion is false, it is not clear why when the hypothesis is false, the conditional statement is **always true**. To try to explain why this is this case, we consider another example. Example 1.3.

## What is the truth value of the statement when the hypothesis and conclusion is false?

If the hypothesis is true and the conclusion is true, the conditional statement if p, then q is true. If the hypothesis is true but the conclusion is false, **the statement is false**.

## What is the truth value of the conditional statement when the hypothesis is true and?

The conditional statement P→Q means that **Q is true whenever P is true**. It says nothing about the truth value of Q when P is false. Using this as a guide, we define the conditional statement P→Q to be false only when P is true and Q is false, that is, only when the hypothesis is true and the conclusion is false.

## Is a declarative sentence that can be meaningfully classified as either true or false?

**A proposition or statement** is a declarative sentence that can be classified as either true or false but not both.