Q$1$: $(20$ points$)$ Minimize the following function using Boolean Algebra specify the Laws you used at each step:

$a+a$ a$\text{'}$b $(5$ points$)$

$a(a^{\text{'}}+b)(5$ points$)$

Show that, $ab+a{b}^{\text{'}}c=ab+ac(5$ points$)$

Show that, $(a+b)(a+b^{\text{'}}+c)=a+bc(5$ points$)$