$2\mathrm{.}1)$ Prove the following theorems algebraically using Boolean Laws:

$2\mathrm{.}1)$ Prove Algebraically:

a$)x(x^{\text{'}}+Y)=xY$

b$)$

$xY+xY\text{'}=x$

c$)xY+x{Y}^{\text{'}}=x$

d$)$

$(A+B)(A+B^{\text{'}})=A$