Question $2.$ Logical Equivalence $[18$ MARKs$]$

For each of the following pairs of expressions, either prove that the two expressions are equivalent or prove that

they are not. Do not use truth tables.

$(ab{)}^{{?}^{?}}(ac)$ and $a(b^{{?}^{?}}c)$

$(ab)vv(ac)$ and $a(bvvc)$

$(ac{)}^{{?}^{?}}(bc)$ and $(a^{{?}^{?}}b)c$

$(ac{)}^{{?}^{?}}(bc)$ and $(avvb)c$

$(ac)vv(bc)$ and $(a^{{?}^{?}}b)c$

$(ac)vv(bc)$ and $(avvb)c$