Answer to Question #179960 in Discrete Mathematics for Yin BSPFNEJE

Question

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

Answer 1

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