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

In math, **a certain statement is true if it’s a correct statement, while it’s considered false if it is incorrect**. And if the truth of the statement depends on an unknown value, then the statement is open.

## How do you know that the statement is true?

Correspondence definition: a statement is true **if and only if it matches reality**. Coherence definition: a statement is true if and only if it coheres or “fits” with other established truths.

## Is every statement true or false?

**every statement is either true or false**; these two possibilities are called truth values. An argument in which it is claimed that the conclusion follows necessarily from the premises. In other words, it is claimed that under the assumption that the premises are true it is impossible for the conclusion to be false.

## What makes a certain statement false?

A false statement **need not be a lie**. A lie is a statement that is known to be untrue and is used to mislead. A false statement is a statement that is untrue but not necessarily told to mislead, as a statement given by someone who does not know it is untrue.

## Is statement both true and false?

**A statement is true if what it asserts is the case, and it is false if what it asserts is not the case**. For instance, the statement “The trains are always late” is only true if what it describes is the case, i.e., if it is actually the case that the trains are always late.

## What is a statement that is either true or false but not both?

Statement: a sentence that is either true or false, but not both. It is also called **a proposition**.

## What is a true or false statement?

A true-false statement is **any sentence that is either true or false but not both**. A negation of a statement has the opposite meaning of a truth value. A negations is written as ~p. If we call the statement: cucumbers are green, p then: p: cucumbers are green – this statement is true.

## Which of the following statements is false?

Discussion Forum

Que. | Which one of the following statements if FALSE? |
---|---|

b. | A relation in which every key has only one attribute is in 2NF |

c. | A prime attribute can be transitively dependent on a key in a 3 NF relation |

d. | A prime attribute can be transitively dependent on a key in a BCNF relation |

## Why is a conditional statement true when the hypothesis is false?

**the hypothesis does not hold**. Therefore, the conditional is true. This example implies that a conditional statement is false only when the hypothesis is true and the conclusion is false.

## Can a conditional statement be 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”.

## What is a true conditional statement?

Definition. A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences. For this conditional statement, P is called the hypothesis and Q is called the conclusion. Intuitively, “If P then Q” means that **Q must be true whenever P is true**.

## How do you prove a conditional statement?

There is another method that’s used to prove a conditional statement true; it **uses the contrapositive of the original statement**. The contrapositive of the statement “If (H), then (C)” is the statement “If (the opposite C), then (the opposite of H).” We sometimes write “not H” for “the opposite of H.”

## Is the statement true or false you can prove a universal conditional is true by Contraposition if and only if you can prove it is true by contradiction?

The law of contraposition says that **a conditional statement is true if, and only if, its contrapositive is true**.

Comparisons.

name | form | description |
---|---|---|

converse | if Q then P | reversal of both statements |

contrapositive | if not Q then not P | reversal and negation of both statements |

## How do you prove for all statements?

**Following the general rule for universal statements, we write a proof as follows:**

- Let be any fixed number in .
- There are two cases: does not hold, or. holds.
- In the case where. does not hold, the implication trivially holds.
- In the case where holds, we will now prove . Typically, some algebra here to show that .