Kenneth Rosen Edition 7 Exercise 1.3 Question 33 (Page No. 35)

Question

Show that $(p \rightarrow q) \rightarrow (r \rightarrow s) $ and $(p \rightarrow r) \rightarrow (q \rightarrow s)$ are not logically equivalent.

Answer 1

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Comments

So we can solved this way without using logical and or operator?

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Yes , we can solve using truth table also.

But it is time cansuming .

Answer 2

In (p$\rightarrow$q)$\rightarrow$(r$\rightarrow$s) $\not\equiv$ (p$\rightarrow$r)$\rightarrow$(q$\rightarrow$s) 

If p=F, q=F, r=T, s=F then LHS is false and RHS is true. 

Hence,they are not logically equivalent.