Do statements have to be true or false?
Statements can be either false or true, but not both at the same time and in the same context. If a statement is offered as both false and true, it violates the Aristotelian Law of Noncontradiction. A statement can be written in a contradictory way in the context of what is possible.
Is there any possibility that a true statement can be false or vice versa?
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).
What is the truth value of the conditional statement when the hypothesis is true and the conclusion is false?
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. To try to explain why this is this case, we consider another example. Example 1.3.
Why is a conditional with a false hypothesis always true?
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. , logical intuitionist. Originally Answered: Why is a conditional statement with a false hypothesis always true? Yes, this is a TRUE statement.
Can statements be false?
As such, a statement is an assertion that something is or is not the case. A statement is true if what it asserts is the case, and it is false if what it asserts is not the case.
Is a statement that is either true or false but not both?
Statement: a sentence that is either true or false, but not both. It is also called a proposition.
Are all mathematical statements either true or false?
Brielfy a mathematical statement is a sentence which is either true or false. For example “The square root of 4 is 5″ is a mathematical statement (which is, of course, false). In mathematics we use language in a very precise way, and sometimes it is slightly different from every day use.
What is contra positive statement?
More specifically, the contrapositive of the statement “if A, then B” is “if not B, then not A.” A statement and its contrapositive are logically equivalent, in the sense that if the statement is true, then its contrapositive is true and vice versa.
What is the true value of the conditional statement when the hypothesis is true and the conclusion is true?
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.
What is the truth value of the conditional statement?
The truth value of a conditional statement can either be true or false. In order to show that a conditional is true, just show that every time the hypothesis is true, the conclusion is also true. To show that a conditional is false, you just need to show that every time the hypothesis is true, the conclusion is false.
Is conditional statement false?
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 |
Which conditional statement is always true?
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 |