Use a K$-$map to find a minimal expansion as a Boolean sum of Boolean products of the Boolean variables x and y for the function below.

a$)$ xy$+$x$$y$+$x$$y$$

b$)$ xy$$z$+$xy$$z$+$x$$yz$+$x$$y$$z$+$x$$y$$z

c$)$ wxyz$+$wx$$yz$+$w$$x$$yz$+$w$$xyz$+$wx$$yz$+$w$$x$$yz$+$w$$xyz$+$w$$xy$$z$+$w$$xy$$z