What is logical equivalence and examples?

In mathematics, two statements and are often said to be logically equivalent, if they are provable from each other given a set of axioms and presuppositions. For example, the statement ” is divisible by 6″ can be regarded as equivalent to the statement “

What is logically equivalent statement?

Definition. Two expressions are logically equivalent provided that they have the same truth value for all possible combinations of truth values for all variables appearing in the two expressions. In this case, we write X≡Y and say that X and Y are logically equivalent.

What is equivalence in discrete mathematics?

Two logical expressions are said to be equivalent if they have the same truth value in all cases. Sometimes this fact helps in proving a mathematical result by replacing one expression with another equivalent expression, without changing the truth value of the original compound proposition.

How do you use logical equivalence?

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. p⇒q≡¯q⇒¯pandp⇒q≡¯p∨q.

How do you find the logical equivalent?

p q and q p have the same truth values, so they are logically equivalent. To test for logical equivalence of 2 statements, construct a truth table that includes every variable to be evaluated, and then check to see if the resulting truth values of the 2 statements are equivalent.

How do you find logical equivalence?

Why do we use logical equivalence?

Because tautologies and contradictions are essential in proving or verifying mathematical arguments, they help us to explain propositional equivalences — statements that are equal in logical argument. And it will be our job to verify that statements, such as p and q, are logically equivalent.