When the hypothesis in a conditional statement is false What is the truth value of this conditional statement?
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When the hypothesis in a conditional statement is false What is the truth value of this conditional statement?
The conditional statement P→Q means that Q is true whenever P is true. It says nothing about the truth value of Q when P is false. Using this as a guide, we define the conditional statement P→Q to be false only when P is true and Q is false, that is, only when the hypothesis is true and the conclusion is false.
Is the conditional statement true or false?
, is called the consequent. A conditional is considered true when the antecedent and consequent are both true or if the antecedent is false. When the antecedent is false, the truth value of the consequent does not matter; the conditional will always be true….Conditional.
| P | Q | P ⇒ Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
Can a conditional have a hypothesis?
A conditional statement (also called an if-then statement) is a statement with a hypothesis followed by a conclusion. The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement. The conclusion is the result of a hypothesis.
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 is the truth value of the conditional having false hypothesis and true conclusion?
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….Definition: A Conditional Statement is…
| p | q | p q |
|---|---|---|
| F | T | T |
| F | F | T |
What is the truth value if the hypothesis is false and the conclusion is true?
If the hypothesis is true and the conclusion is true, the conditional statement if p, then q is true. If the hypothesis is true but the conclusion is false, the statement is false.
What is conditional hypothesis?
Conditional statements are those statements where a hypothesis is followed by a conclusion. It is also known as an ” If-then” statement. If the hypothesis is true and the conclusion is false, then the conditional statement is false. Likewise, if the hypothesis is false the whole statement is false.
What is a conditional statement example?
Conditional Statement: “If today is Wednesday, then yesterday was Tuesday.” Hypothesis: “If today is Wednesday” so our conclusion must follow “Then yesterday was Tuesday.”
What does q → P mean?
Converse, Contrapositive. The converse of a conditional proposition p → q is the proposition q → p. As we have seen, the bi- conditional proposition is equivalent to the conjunction of a conditional proposition an its converse.
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 the hypothesis 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.
Why is the contrapositive true?
If a statement is true, then its contrapositive is true (and vice versa). If a statement is false, then its contrapositive is false (and vice versa). If a statement’s inverse is true, then its converse is true (and vice versa). If a statement’s inverse is false, then its converse is false (and vice versa).
When can a conditional statement be 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.
What is the truth value of conditional statement when the hypothesis is false and the conclusion is true?
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….Definition: A Conditional Statement is…
| p | q | p q |
|---|---|---|
| F | F | T |
