1) a*(a+b+c) = aa+ab+ac = a+ab+ac = a(1 + b + c) = a * 1 = a
2) a*b + ¬b + ¬a*b = b(a + ¬a) + ¬b = b * 1 + ¬b = b + ¬b =1
3) (¬a + b) * ¬c * (c + a * ¬b) = (¬a + b) * (¬c*c + a¬b¬c) =
(¬a + b) * a¬b¬c = ¬aa¬b¬c + ba¬b¬c = 0 + 0 = 0
4) (a+b)*(¬a+b)*(¬a + ¬b) = (¬aa+ab+¬ab+b)*(¬a + ¬b) =
(ab + ¬ab + b)*(¬a + ¬b) = b(a + ¬a + 1)*(¬a + ¬b) = b*(¬a + ¬b) =
¬ab + ¬bb = ¬ab
1) a*(a+b+c) = aa+ab+ac = a+ab+ac = a(1 + b + c) = a * 1 = a
2) a*b + ¬b + ¬a*b = b(a + ¬a) + ¬b = b * 1 + ¬b = b + ¬b =1
3) (¬a + b) * ¬c * (c + a * ¬b) = (¬a + b) * (¬c*c + a¬b¬c) =
(¬a + b) * a¬b¬c = ¬aa¬b¬c + ba¬b¬c = 0 + 0 = 0
4) (a+b)*(¬a+b)*(¬a + ¬b) = (¬aa+ab+¬ab+b)*(¬a + ¬b) =
(ab + ¬ab + b)*(¬a + ¬b) = b(a + ¬a + 1)*(¬a + ¬b) = b*(¬a + ¬b) =
¬ab + ¬bb = ¬ab