2. [12 marks] This question involves Boolean algebra. Solutions must show sequential equivalent Boolean expressions. Moving from one expression to the next in the proof must include a justification requiring no

more than two rules. You may only use the the Boolean laws covered in the slides, and the distributive law for OR that was part of Tutorial 1, as justification. (a) Prove: (¬AA¬BA¬C) V (AA¬BA¬C) V (AA¬BA C) = ¬BA (AA (b) Simplify the following Boolean expression as much as possible. An expression that is simpler than another will have fewer Boolean operators. Parenthesis are not Boolean operators. AAB V ((AVC) A B A (A V C)) V (A V B) (c) Simplify the following Boolean expression as much as possible. An expression that is simpler than another will have fewer Boolean operators. Parenthesis are not Boolean operators. (A A BA¬C) V (AA¬BAC) V (AAD) V (AAB) V (A V D) Submit the file a1q2.pdf.