Simplify the following expressions using Boolean algebra. a$.$ A $+$ AB b$.$ AB $+$ AB$\text{'}$ c$.$ A'BC $+$ AC d$.$ A$\text{'}$B $+$ ABC' $+$ ABC Simplify the following expressions using Boolean algebra. a$.$ AB $+$ A$($CD $+$ CD$\text{'})$ b$.($BC$\text{'}+$ A$\text{'}$D$)($AB$\text{'}+$ CD$\text{'})$ Using DeMorgan's theorem, show that: a$.($A $+$ B$)\text{'}($A$\text{'}+$ B$\text{'})\text{'}=0$ b$.$ A $+$ A$\text{'}$B $+$ A$\text{'}$B$\text{'}-1$