Logical equivalence is different from material equivalence, although the two concepts are intrinsically related. The logical equivalence of $${\displaystyle p}$$ and $${\displaystyle q}$$ is sometimes expressed as $${\displaystyle p\equiv q}$$, $${\displaystyle p::q}$$, $${\displaystyle {\textsf {E}}pq}$$, or $${\displaystyle p\iff q}$$, depending on the notation being used. Propositional Logic Grinshpan Examples of logically equivalent statements Here are some pairs of logical equivalences. In logic and mathematics, statements $${\displaystyle p}$$ and $${\displaystyle q}$$ are said to be logically equivalent if they are provable from each other under a set of axioms, or have the same truth value in every model. But the logical equivalences \(p\vee p\equiv p\) and \(p\wedge p\equiv p\) are true for all \(p\). p = It … Equivalence statements. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Share ← → In this tutorial we will cover Equivalence Laws. Boolean Algebra. De Morgan’s laws: When we negate a disjunction (respectively, a conjunction), we have to negate the two logical statements, and change the operation from disjunction to conjunction (respectively, from conjunction to a disjunction). Example Following are two statements. Two statements are said to be equivalent if they have the same truth value. Each may be veri ed via a truth table. Propositional Logic Equivalence Laws.