Why is it that when A is false and B is false, we infer that A->B is true?

What Proposition logic that will give false if A is true and B is false?

Negation (¬) − The negation of a proposition A (written as ¬A) is false when A is true and is true when A is false. Implication / if-then (→) − An implication A→B is the proposition “if A, then B”.
Connectives.

A B A → B
True False False
False True True
False False True

Is there a statement that is both true and false?

Dialetheism (from Greek δι- di- ‘twice’ and ἀλήθεια alḗtheia ‘truth’) is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called “true contradictions”, dialetheia, or nondualisms.

What is the meaning of a implies B?

“A implies B” means that B is at least as true as A, that is, the truth value of B is greater than or equal to the truth value of A. Now, the truth value of a true statement is 1, and the truth value of a false statement is 0; there are no negative truth values.

What is a implies b equal to?

In other words, A and B are equivalent exactly when both A ⇒ B and its converse are true. • (A implies B) ⇔ (¬B implies ¬A). In other words, an implication is always equivalent to its contrapositive.

What is a proposition that is always false?

A compound proposition is called a contradiction if it is always false, no matter what the truth values of the propositions (e.g., p A ¬p =T no matter what is the value of p.

How do you tell if a proposition is true or false?

The proposition p ↔ q, read “p if and only if q”, is called bicon- ditional. It is true precisely when p and q have the same truth value, i.e., they are both true or both false.

What does P → Q mean?

In conditional statements, “If p then q” is denoted symbolically by “p q”; p is called the hypothesis and q is called the conclusion. For instance, consider the two following statements: If Sally passes the exam, then she will get the job.

What is the truth value of the statement when the hypothesis is false and conclusion is false?

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.
Definition.

P Q P→Q
T T F F T F T F T F T T

Is the assertion This statement is false a proposition?

In propositional logic, a proposition is a statement that is either true or false, but not both. In a text I am reading and in many others, “this statement is false” is not considered a proposition.

Which is the statement is false?

A false statement need not be a lie. A lie is a statement that is known to be untrue and is used to mislead. A false statement is a statement that is untrue but not necessarily told to mislead, as a statement given by someone who does not know it is untrue.

Is statement always false?

Contradiction: A statement form which is always false.

Which is false statement about value proposition?

If our original proposition is false, then its negation is true. If our original proposition is true, then its negation is false.
Truth Value.

p NOT p
F T

Why is it that sentences have no truth value?

[A sentence which cannot be said to be true or false is without truth value, and therefore does not assert a “statement.” Questions and commands, for example are genuine sentences, but do not assert statements and thus have no truth value.]

How is truth value determined?

The truth or falsity of a proposition is called its truth value . The truth value of a compound proposition can be calculated from the truth values of its components, using the following rules: For a conjunction to be true, both conjuncts must be true. For a disjunction to be true, at least one disjunct must be true.