Chapter 1.3, Problem 37E

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

The dual of a compound proposition that only the logical operators $\vee ,\wedge$and $\neg$is the compound proposition obtained by replacing each $\vee$by $\wedge$, each $\wedge$by $\vee$, each T by F, and each F by T. The dual ofsis denoted bys*.