Why is a conditional true when the hypothesis is false?
Table of Contents
- 1 Why is a conditional true when the hypothesis is false?
- 2 Why is a conditional statement with a false antecedent always true?
- 3 What is a conditional statement that is always true called?
- 4 What makes a conditional false is a false antecedent and a false consequent?
- 5 What does trivially true mean?
- 6 Is the conditional True or false?
Why is a conditional true when the hypothesis is false?
the hypothesis does not hold. Therefore, the conditional is true. This example implies that a conditional statement is false only when the hypothesis is true and the conclusion is false. This conditional statement is true yet its hypothesis is false and its conclusion is true.
Why is a conditional statement with a false antecedent always true?
When the antecedent is false, the truth value of the consequent does not matter; the conditional will always be true. A conditional is considered false when the antecedent is true and the consequent is false….Conditional.
| P | Q | P ⇒ Q |
|---|---|---|
| F | F | T |
What is a conditional statement that is always true called?
5 Cards in this Set
| A compound statement that is always true is called a/an | Tautology |
|---|---|
| Conditional statements that are always true are called? | Implications |
| A compound statement that is always false is called a/an? | Self contradiction |
| A biconditional statement p <->q is true when? | P and q have the same truth value |
What is a conditional statement that is false but has a true inverse?
Negating both the hypothesis and conclusion of a conditional statement. For example, the inverse of “If it is raining then the grass is wet” is “If it is not raining then the grass is not wet”. Note: As in the example, a proposition may be true but its inverse may be false.
What if hypothesis is false?
The science experiment is designed to disprove or support the initial hypothesis. When the findings do not align with the hypothesis, the experiment is not a failure. When the results do not agree with the hypothesis, record the information just as if it did support the original hypothesis.
What makes a conditional false is a false antecedent and a false consequent?
Conditional statement: an “if p, then q” compound statement (ex. A conditional asserts that if its antecedent is true, its consequent is also true; any conditional with a true antecedent and a false consequent must be false.
What does trivially true mean?
ago. Additional comment actions. “Trivial” just means it’s a really, really easy proof. “Vacuous” is stronger: a statement is vacuously true if the proof basically boils down to a statement about every element of an empty set.
Is the conditional True or false?
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….Definition: A Conditional Statement is…
| p | q | p q |
|---|---|---|
| F | T | T |
| F | F | T |
When a conditional and its converse are true?
when a conditional and its converse are true, you can combine them as a true statement; an if and only if. if a conditional is true and its hypothesis is true, then its conclusion is true.
When the hypothesis is false and the conclusion is true?
Hypotheses followed by a conclusion is called an If-then statement or a conditional statement. This is read – if p then q. A conditional statement is false if hypothesis is true and the conclusion is false.