Propositional Logic Grinshpan Examples of logically equivalent statements Here are some pairs of logical equivalences. Propositional Logic Equivalence Laws. Boolean Algebra. Equivalence statements. p = It … Example Following are two statements. Share ← → In this tutorial we will cover Equivalence Laws. 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 \(p\). Logical equivalence is different from material equivalence, although the two concepts are intrinsically related. Each may be veri ed via a truth table. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. 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). 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. Two statements are said to be equivalent if they have the same truth value.