What does it mean if two statements are logically equivalent?
Two statement forms are logically equivalent if, and only if, their resulting truth tables are identical for each variation of statement variables.
What does it mean the statements are equivalent?
Equivalent Statements are statements that are written differently, but hold the same logical equivalence. Case 1: “ If p then q ” has three equivalent statements.
How do you prove something is logically equivalent?
Two logical statements are logically equivalent if they always produce the same truth value. Consequently, p≡q is same as saying p⇔q is a tautology. Beside distributive and De Morgan’s laws, remember these two equivalences as well; they are very helpful when dealing with implications.
What is logically 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 an example of an equivalent?
Two or more fractions are said to be equivalent if they are equal to the same fraction when simplified. For example, the equivalent fractions of 1/5 are 5/25, 6/30, and 4/20, which on simplification, result in the same fraction, that is, 1/5.
Are the two statements equivalent?
Logical equivalence occurs when two statements have the same truth value. This means that one statement can be true in its own context, and the second statement can also be true in its own context, they just both have to have the same meaning.
What does logically equivalent mean in math?
Logical Equivalence. Definition. Two statement forms are called logically equivalent if, and only if, they have identical truth values for each possible substitution for their. statement variables.
What is logical equivalence in discrete mathematics?
Logical equivalence is a type of relationship between two statements or sentences in propositional logic or Boolean algebra. A proposition is a declarative sentence (a sentence that declares a fact) that is either true or false. Examples of propositions: Tallahassee is the capital of Florida.