Table of Contents
What does it mean to interchange a hypothesis and conclusion?
Interchanging involves switching the hypothesis and conclusion so that the hypothesis becomes the conclusion and the conclusion becomes the hypothesis. So if the equation of a conditional is p → q (if p, then q), the equation of its inverse is q → p (if q, then p).
What is converse and contrapositive?
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 type of implication is formed by interchanging the hypothesis and the conclusion?
contrapositive
And the contrapositive is formed by interchanging the hypothesis and conclusion and then negating both.
What is negation of the hypothesis?
The negation of a true statement is false, and the negation of a false statement is true. Examples: 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.
How do you identify a hypothesis a conclusion?
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.
What is the example of hypothesis and conclusion?
Determine the hypothesis and conclusion: I’ll bring an umbrella if it rains. Hypothesis: “It rains.” Conclusion: “I’ll bring an umbrella.”
Which is the inverse of P → Q?
The inverse of p → q is ¬p → ¬q. If p and q are propositions, the biconditional “p if and only if q,” denoted by p ↔ q, is true if both p and q have the same truth values and is false if p and q have opposite truth values.
How do you negate a hypothesis?
To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion. The inverse of “If it rains, then they cancel school” is “If it does not rain, then they do not cancel school.”…Converse, Inverse, Contrapositive.
| Statement | If p , then q . |
|---|---|
| Contrapositive | If not q , then not p . |