Consider this NAND operator uarr, which is defined as follows puarrq$-=$not$(p^{{?}^{?}}q).$ We haven't seen this operator in our class lecture but it works like NOT$-$AND.

$(1)(3$ points$)$ Using truth tables show that ${?}^{{?}^{?}}$ is associative, i$.$e$.,p^{{?}^{?}}(q^{{?}^{?}}r)-=(p^{{?}^{?}}q{)}^{{?}^{?}}r.$