§ 5.3 Indirect proof: proof by contradiction In a proof by contradiction, one assumes that one’s conclusion is false, and then tries to show that this assumption (together with the argument’s premises) leads to a contradiction.
How do you prove contrapositive?
“If A, then B.” The second statement is called the contrapositive of the first. Instead of proving that A implies B, you prove directly that ¬B implies ¬A.
When should you use proof by contrapositive?
… whenever you are given an “or” statement, you will always use proof by contraposition. Why? Because trying to prove an “or” statement is extremely tricky, therefore, when we use contraposition, we negate the “or” statement and apply De Morgan’s law, which turns the “or” into an “and” which made our proof-job easier!
What is a contrapositive statement example?
For example, consider the statement, “If it is raining, then the grass is wet” to be TRUE. Then you can assume that the contrapositive statement, “If the grass is NOT wet, then it is NOT raining” is also TRUE.
Is proof by contradiction the same as contrapositive?
In a proof by contrapositive, we actually use a direct proof to prove the contrapositive of the original implication. In a proof by contradiction, we start with the supposition that the implication is false, and use this assumption to derive a contradiction. This would prove that the implication must be true.
What is the contrapositive of P → Q?
Contrapositive: The contrapositive of a conditional statement of the form “If p then q” is “If ~q then ~p”. Symbolically, the contrapositive of p q is ~q ~p. A conditional statement is logically equivalent to its contrapositive.
What is meant by contrapositive?
Definition of contrapositive
: a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and interchanging them “if not-B then not-A ” is the contrapositive of “if A then B “
Which one is the contrapositive of Q → P Mcq?
Explanation: q whenever p contrapositive is ¬q → ¬p.
Which is logically equivalent to P ↔ Q?
P → Q is logically equivalent to ¬ P ∨ Q . Example: “If a number is a multiple of 4, then it is even” is equivalent to, “a number is not a multiple of 4 or (else) it is even.”
What is converse contrapositive and inverse of the statement P → Q?
The converse of the conditional statement is “If Q then P.” The contrapositive of the conditional statement is “If not Q then not P.” The inverse of the conditional statement is “If not P then not Q.”
What is a converse statement example?
A converse statement is gotten by exchanging the positions of ‘p’ and ‘q’ in the given condition. For example, “If Cliff is thirsty, then she drinks water” is a condition. The converse statement is “If Cliff drinks water, then she is thirsty.”
What’s a converse statement?
Definition: The converse of a conditional statement is created when the hypothesis and conclusion are reversed. In Geometry the conditional statement is referred to as p → q. The Converse is referred to as q → p.