Problem $2($Boolean Function Table$).$ Solve each of the following problem constructing the necessary Truth table.

A four input function $z(x_1,x_2,x_3,x_4)$ has the value $1$ if and only if either of the following two conditions holds: a$)$ all the inputs have the same value; b$)$ half the inputs are $0$s and half are $1$s$.$ Determine whether or not $z$ has a single gate realization using a standard gate type $($with input $/$ output inversions needed$).$ Standard GATE type includes AND, OR$,$ NOT, XOR, and XNOR gates. $[$Points : $5]$