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

, is called the consequent. **A conditional is considered true when the antecedent and consequent are both true or if the antecedent is false**.

## Why is an implication true if the antecedent is false?

That is, a true antecedent/premise/condition (P) can only imply a true /consequent/conclusion/consequence (Q). **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.

## What happens if a conditional statement 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 the antecedent of a conditional statement?

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.

## Is the conditional True or false?

Summary: A conditional statement, symbolized by p q, is an if-then statement in which p is a hypothesis and q is a conclusion. **The conditional is defined to be true unless a true hypothesis leads to a false conclusion**.

Definition: A Conditional Statement is…

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

F | T | T |

F | F | T |

## 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.

## Under which unique condition will an implication be false?

An implication is the compound statement of the form “if p, then q.” It is denoted p⇒q, which is read as “p implies q.” It is false only when **p is true and q is false**, and is true in all other situations.

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

Python if Statement is used for decision-making operations. It contains a body of code which runs only when the condition given in the if statement is true. If the condition is false, then **the optional else statement runs which contains some code for the else condition**.

## What conditional statement is formed if both parts of the conditional are negated?

Contrapositive Statement

**Contrapositive Statement**

The contrapositive of a conditional statement is a combination of the converse and the inverse. The “If” part or p is replaced with the “then” part or q and the “then” part or q is replaced with the “If” part or p. After that, both parts are negated.

## 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 a compound statement that is always false?

**A self-contradiction** is a compound statement that is always false.

## When the compound statement is false for all its components then the statement is called?

There are two cases in which compound statements can be made that result in either always true or always false. These are called **tautologies and contradictions**, respectively. Let’s consider a tautology first, and then a contradiction: Example 1.1.

## What are conditional statements that are always true called?

5 Cards in this Set

A compound statement that is always true is called a/an | Tautology |
---|---|

Conditional statements that are always true are called? | Implications |

A compound statement that is always false is called a/an? | Self contradiction |

A biconditional statement p <->q is true when? | P and q have the same truth value |

## Which statement is always false?

Contradiction: A statement form which is always false.

## What is a statement that is either true or false?

**Proposition** is simply a statement that is either true or false, has no variables involved. But predicates can take variables, and once we replace the variable by a constant, it becomes a proposition.

## Is the assertion This statement is false a proposition?

In propositional logic, a proposition is a statement that is either true or false, but not both. In a text I am reading and in many others, “this statement is false” is **not considered a proposition**.