To check whether P entails Q, check whether (P ∧ ¬Q) is satisfiable — if so, then P does not entail Q. Similarly check whether (¬P ∧ Q) is satisfiable. If neither is satisfiable, then the formulas are equivalent.

How do you know if two expressions 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 explain logical equivalence?

Logical equivalence is a type of relationship between two statements or sentences in propositional logic or Boolean algebra. The relation translates verbally into “if and only if” and is symbolized by a double-lined, double arrow pointing to the left and right ( ).

What is logical equivalent example?

Now, consider the following statement: If Ryan gets a pay raise, then he will take Allison to dinner. This means we can also say that If Ryan does not take Allison to dinner, then he did not get a pay raise is logically equivalent.

How do you know if a truth table is logically equivalent?

So the way we can use truth tables to decide whether. The left side is logically equivalent to the right it's just to make a truth table for each one and see if it works out the same.

Are the statements P ∧ Q ∨ R and P ∧ Q ∨ R logically equivalent?

Since columns corresponding to p∨(q∧r) and (p∨q)∧(p∨r) match, the propositions are logically equivalent. This particular equivalence is known as the Distributive Law.