1. Show using the Boolean Algebra (Use Truth Tables) the following:
(1) 1 + a = 1
(2) a.a'= 0
(3) a + b + c = c + b + a
(4) (1 + 0)' = 0
(5) (1 . 1)' = 1
(6) a + a' = 1
(7) b.b'=0
(8) (a'.b)+(a.b)=b
2. Use logic symbols(gates)for and, not/invert and or to define a Logic Circuit to calculate the following expressions:
(i) y = a + b
(ii) x = a.b' + a'.b
3. Build one logic circuit to be able to calculate both x and y, see (i) and (ii) in 2.