Exercise on Boolean Algebra

$1.$ Given the Boolean expression F $=$ A$\text{'}$B $+$ AB $+$ AC$,$ simplify the expression using Boolean algebraic laws.

$2.$ Simplify the Boolean expression G $=($A $+$ B$\text{'})($A$\text{'}+$ C$)($A$\text{'}+$ B $+$ C$).$

$3.$ Simplify the expression H $=$ A$($B$\text{'}+$ C$)+$ AB $+$ AC$.$

$4.$ Evaluate the following expression for A $=1,$ B $=0,$ and C $=1$: F $=$ A$($B$\text{'}+$ C$\text{'})($A $+$ B$)($B$\text{'}+$ C$).$

$5.$ Convert the following Boolean expression into its canonical SOP $($Sum of Products$)$ form: G $=($A $+$ B$\text{'})($A$\text{'}+$ C$)($A$\text{'}+$ B $+$ C$).$