Use a K$-$map to find a minimal expansion as a Boolean sum of Boolean products of each of these functions of the Boolean variables x and y$.$ Then find the same expression using the Quine$-$McCluskey method.

a$)$ x$\text{'}$y $+$ x$\text{'}$y$\text{'}$

b$)$ xy $+$ xy$\text{'}$

c$)$ xy $+$ xy$\text{'}+$ x$\text{'}$y $+$ x$\text{'}$ y$\text{'}$