Question #179960

For propositions p, q, and r, determine whether 𝑝 ⟶ (𝑞 ⟶ 𝑟) and (𝑝 ⟶ 𝑞) ⟶ 𝑟 are logically equivalent.


1
Expert's answer
2021-04-13T13:46:51-0400

If p=q=s=F,|p|=|q |=|s|=F, then 𝑝(𝑞𝑟)=F(FF)=FT=T|𝑝 \to (𝑞 \to 𝑟)|=F \to (F \to F)=F\to T=T but (𝑝𝑞)𝑟=(FF)F=TF=F|(𝑝 \to 𝑞) \to 𝑟|=(F \to F) \to F=T\to F=F, and we conclude that the formulas are not logically equivalent.


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