In the truth table above, p q is only false when the hypothesis (p) is true and the conclusion (q) is false; otherwise it is true. Note that a conditional is a compound statement. Now that we have defined a conditional, we can apply it to Example 1….Search form.

p q p q
T F F
F T T
F F T

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

Conditionals: Another way of thinking about conditional sentences is as “or” sentences. The not applies only to the first sentence, as in “(not P) or Q”. These conditional statements will then be true any time the hypothesis (“P”) is false, because “not P” will be true.

## When a conditional and its converse are true?

When a conditional and its converse are true, you can combine them as a true biconditional. A biconditional statement is said to be true when both parts have the same truth value, i.e. both the conditional and its converse are true.

## What is a negation of a conditional statement?

The negation of a conditional statement is only true when the original if-then statement is false. The negation of a conjunction is only false when the original two statements are both true. The negation of a disjunction is only true when both of the original statements are false.

## How do you negate a conditional?

Negation of a Conditional By definition, p → q is false if, and only if, its hypothesis, p, is true and its conclusion, q, is false. It follows that the negation of “If p then q” is logically equivalent to “p and not q.”

## Is it true that the negation of a conditional statement is also conditional statement?

The negation of the conditional statement “p implies q” can be a little confusing to think about. Let’s get started with an important equivalent statement to the conditional. One way to write the conditional is: “if p, then q”. Thus, if you know p, then the logical conclusion is q.

## What is the contrapositive of the conditional statement?

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of “If it rains, then they cancel school” is “If they do not cancel school, then it does not rain.” If p , then q .

## What is P -> Q?

The statement “p implies q” means that if p is true, then q must also be true. The statement “p implies q” is also written “if p then q” or sometimes “q if p.” Statement p is called the premise of the implication and q is called the conclusion. You can view Statement 1 above as a promise.

## What is the hypothesis statement?

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study.