# How does one prove a generalised conditional statement?

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## 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.”

## What is the general form of a conditional statement?

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.

## What makes a conditional statement true?

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.

## What is meant by the rule of conditional proof demonstrate with an example?

A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent.
Symbolic logic.

1. A → B (“If A, then B”)
3. A (conditional proof assumption, “Suppose A is true”)

## How do you prove all statements?

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

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

## How do you prove a conditional statement 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.

## Is a conditional statement always true?

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.

## When conditions in an if/then test tests true?

When executing a block If (2nd syntax), condition is tested. If condition is true, then the statements following Then are executed. If condition is false, then each ElseIf (if any) is evaluated in turn. If a true condition is found, then the statements following the associated Then are executed.

## How will you identify the hypothesis and conclusion of a conditional statement?

SOLUTION: The hypothesis of a conditional statement is the phrase immediately following the word if. The conclusion of a conditional statement is the phrase immediately following the word then. Hypothesis: Two lines form right angles Conclusion: The lines are perpendicular.

## How do you prove a logical statement?

In general, to prove a proposition p by contradiction, we assume that p is false, and use the method of direct proof to derive a logically impossible conclusion. Essentially, we prove a statement of the form ¬p ⇒ q, where q is never true. Since q cannot be true, we also cannot have ¬p is true, since ¬p ⇒ q.

## How do you prove a statement in discrete mathematics?

First and foremost, the proof is an argument. It contains sequence of statements, the last being the conclusion which follows from the previous statements. The argument is valid so the conclusion must be true if the premises are true.

## How do you use logical reasoning to prove statements are true?

The trick to using logical reasoning is to be able to support any statement (conjecture) you make with a valid reason. In geometry, we use facts, postulates, theorems, and definitions to support conjectures. Watch the video to see what can go wrong if you don’t support your conjecture.

## Which statement has to be proved before being accepted?

A theorem is a statement that has been proven to be true based on axioms and other theorems.

## Why do we need to prove statements?

Proof explains how the concepts are related to each other. This view refers to the function of explanation. Another reason the mathematicians gave was that proof connects all mathematics, without proof “everything will collapse”. You cannot proceed without a proof.

## What do you call the statement that starts with a general information or agreed assumption?

A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

## What do you call the statement that are assumed to be true and do not need proof?

A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven.

## What do you call the part of a conditional statement that follows then when writing in if/then form?

the conclusion

The part of the statement following if is called the hypothesis , and the part following then is called the conclusion.