Answer to Question #191821 in Discrete Mathematics for Liliey

Question #191821

Using Boolean algebra simplify the statement ยฌ(๐‘Ÿ โ†’ ๐‘ ) โ†’ (ยฌ๐‘Ÿ) 


1
Expert's answer
2021-05-12T01:56:40-0400

Using Boolean algebra let us simplify the statement:


ยฌ(๐‘Ÿโ†’๐‘ )โ†’(ยฌ๐‘Ÿ)=ยฌ(ยฌ(๐‘Ÿโ†’๐‘ ))โˆจ(ยฌ๐‘Ÿ)=(๐‘Ÿโ†’๐‘ )โˆจ(ยฌ๐‘Ÿ)=(ยฌ๐‘Ÿโˆจ๐‘ )โˆจ(ยฌ๐‘Ÿ)=(sโˆจยฌ๐‘Ÿ)โˆจ(ยฌ๐‘Ÿ)=sโˆจ(ยฌ๐‘Ÿโˆจยฌ๐‘Ÿ)=sโˆจยฌ๐‘Ÿ=ยฌ๐‘Ÿโˆจs=๐‘Ÿโ†’๐‘ .ยฌ(๐‘Ÿ โ†’ ๐‘ ) โ†’ (ยฌ๐‘Ÿ) =ยฌ(ยฌ(๐‘Ÿ โ†’ ๐‘ ))\lor (ยฌ๐‘Ÿ) =(๐‘Ÿ โ†’ ๐‘ )\lor (ยฌ๐‘Ÿ) =(ยฌ๐‘Ÿ\lor ๐‘ )\lor (ยฌ๐‘Ÿ) = (s\lor ยฌ๐‘Ÿ)\lor (ยฌ๐‘Ÿ) =s\lor( ยฌ๐‘Ÿ\lor ยฌ๐‘Ÿ) =s\lor ยฌ๐‘Ÿ=ยฌ๐‘Ÿ\lor s=๐‘Ÿ โ†’ ๐‘ .



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