It states that “if A is true, then B must also be true”. This means that **when A is false, the statement doesn’t conclude anything**.

## What type of statement is if A then B?

conditional statement

Conditionals: “if A then B” (or “A implies B”) is a **conditional statement with antecedent A and consequent B**. It’s contrapositive is “if not B then not A” and it’s converse is “if B then A”. Statements with the same truth table are said to be equivalent.

## What does if A then B mean?

A statement of the form “If A, then B” asserts that **if A is true, then B must be true also**. If the statement “If A, then B” is true, you can regard it as a promise that whenever the A is true, then B is true also. Most theorems can be stated in the form “If A, then B.”

## How do you prove that a conditional statement is true?

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.”

## How do you write an IF THEN statement in math?

Use the statement: I will graduate when I pass Calculus. **Rewrite in if-then form and determine the hypothesis and conclusion**. This statement can be rewritten as If I pass Calculus, then I will graduate. The hypothesis is “I pass Calculus,” and the conclusion is “I will graduate.”

## How do you prove an implies B?

To prove A → B, **assume that A is true and prove that B is true**. That is, add A to the fact bank and then proceed to prove B.

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

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**. To show that a conditional is false, you just need to show that every time the hypothesis is true, the conclusion is false.

## Is a B and B C then a C?

An example of a transitive law is “**If a is equal to b and b is equal to c, then a is equal to c**.” There are transitive laws for some relations but not for others.

## Is a B then B A?

Symmetric Property: **if a = b, then b = a**. Transitive Property: if a = b and b = c, then a = c.

## Are inverse statements always true?

If the statement is true, then the contrapositive is also logically true. **If the converse is true, then the inverse is also logically true**. If two angles are congruent, then they have the same measure.

Converse, Inverse, Contrapositive.

Statement | If p , then q . |
---|---|

Inverse | If not p , then not q . |

Contrapositive | If not q , then not p . |

## 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 IF and THEN statement?

Conditional Statements. A conditional statement (also called an If-Then Statement) is **a statement with a hypothesis followed by a conclusion**. Another way to define a conditional statement is to say, “If this happens, then that will happen.” The hypothesis is the first, or “if,” part of a conditional statement.

## What is inverse conditional statement?

The inverse of a conditional statement is **when both the hypothesis and conclusion are negated**; the “If” part or p is negated and the “then” part or q is negated. In Geometry the conditional statement is referred to as p → q. The Inverse is referred to as ~p → ~q where ~ stands for NOT or negating the statement.

## Why is the contrapositive true?

**If a statement is true, then its contrapositive is true** (and vice versa). If a statement is false, then its contrapositive is false (and vice versa). If a statement’s inverse is true, then its converse is true (and vice versa). If a statement’s inverse is false, then its converse is false (and vice versa).

## Which of the following forms is an inverse of if/p then q?

If ~p then ~q

Inverse: Suppose a conditional statement of the form “If p then q” is given. The inverse is “**If ~p then ~q**.” Symbolically, the inverse of p q is ~p ~q.