Explanation

(a)
Since, switches $a$ and $b$ and $a^{'},\ b^{'}$ and $c^{'}$ are parallel which is denoted by $a \land b$ and $a^{'} \land b^{'} \land c^{'}$ respectively
Now, $(a \land b),\ c$ and $(a^{'} \land b^{'} \land c^{'})$ are connected in series, then switching function of complete network is
$(a \land b) \vee c \vee (a^{'} \land b^{'} \land c^{'})$