WHY IS A implies B equivalent to not A or B?

WHY IS A implies B equivalent to not A or B?

A ⇒ B means that if A is true, then B better be true, otherwise who cares. If A is false, then B doesn’t matter.

Is A and B logically equivalent to B and A?

⇔ ((A implies B) and (B implies A)). In other words, A and B are equivalent exactly when both A ⇒ B and its converse are true.

Is A or B equal to not A and not B?

“(not-A) and (not-B)” is the same as “neither A nor B”. Don’t be fooled by the “or” in “nor” — this not a disjunction, it’s a conjunction.

WHAT IS A implies B equivalent to?

For instance, logical implication: A implies B if whenever A is true, B is true too. It’s usually interpreted to mean (see discussion in Section 14.2) that this can only be false when A is true and B is false, so an equivalent proposition is “B or not A”.

How do you write an equivalent statement?

Take for example the statement “If is even, then is an integer.” An equivalent statement is “If is not an integer, then is not even.” The original statement had the form “If A, then B” and the second one had the form “If not B, then not A.” (Here A is the statement ” is even”, so “not A” is the statement ” is not even” …

Are logically equivalent?

Logical Equivalence: Two statements are logically equivalent if, and only if, their resulting forms are logically equivalent when identical statement variables are used to represent component statements.

Which of the following is equivalent to P → Q?

P → Q is logically equivalent to ¬ P ∨ Q . Example: “If a number is a multiple of 4, then it is even” is equivalent to, “a number is not a multiple of 4 or (else) it is even.”

What is equivalent to not A or B?

DeMorgan’s Laws The negation of a conjunction (logical AND) of 2 statements is logically equivalent to the disjunction (logical OR) of each statement’s negation. That sounds like a mouthful, but what it means is that “not (A and B)” is logically equivalent to “not A or not B”.