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.

## logical equivalence laws examples

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