Prove the given expression is a tautology by developing a series of logical equivalence to demonstrate that it is logically equivalent to T.

[(p V q) (p r) (q r)] r

Order Options

_________________ [(p V q) (p r) (q r)] r = [(p V q) (p V q) r] by logical equivalence

_________________ ( (p V q) r ) r by identity law

_________________ ((p V q) r ) r = ((p V q) r ) V r by logical equivalence

_________________ ( p q) V T by negation law

_________________ [ T V ((p V q) r )] r by negation law

_________________ [(p V q) (p r) (q r)] r by associative law

_________________ [((p V q) (p V q) V ((p V q) r )] r by distributive law

_________________ [((p V q) ((p V q) V (p V q) r ) r by distributive law

_________________ T by domination law

_________________ [(p V q) (p r) (q r)] r

_________________ ( p q) V ( r V r) by associative law

_________________ [(p V q) ((p V q) r ) r = [(p V q) ((p V q)V r)] r by logical equivalence

[F V ((p V q) r)] r by negation law

(( p q) V r ) V r by De Morgan's law

( p q) V F by negation law