a) Consider the right hand side of the equation, we have.

1.
(a) Consider the right hand side of the equation, we have
= (X + Y)(X + Z)
= XX + XZ + XY + YZ
From indempotence law,
XX = X
= X + XZ + XY + YZ
= X + XY + XZ + YZ = X(1 + Y) + Z(X + Y)
Now as a property of 1 and 0 we have
1 + Y = 1 we have
= X.1 + Z(X + Y)
From the same property, we rewrite RHS as
= X + XZ + YZ
Factorizing X for the first two terms, we get
= X(1 + Z) + YZ
From the property of 1
1+z=1 hence we have
= X.1 + YZ
Again X.1=X hence
X+XY= Left hand side hence proved.

(b) x y z + x y z+ x y z+ ¿ x y z.
2. ak = 2ak-1 + 3ak-2 + 4k + 6
with initial conditions a0=20 and a1=60.