$($Algebraic manipulation$)$ Minimize the number of operator sin the following

Boolean expressions.

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

b$)($x$+$y$)($x$+$y$\text{'})$

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

d$)$ y$\text{'}$z$\text{'}+$ x$\text{'}$y$\text{'}+$x$\text{'}$z$+$yz$\text{'}$