Question

1. Simplify the following Boolean expressions algebraically.
a) AB + AB'+ A'C + A'C'
b) XY + XYZ' + XYZ' + XZY

Answer 1

Answer:

a) AB + AB'+ A'C + A'C' = 1

b) XY + XYZ' + XYZ' + XZY = XY

Explanation:

a) AB + AB'+ A'C + A'C'

= A(B + B') + A'(C + C')

= A(1) + A' (1)

= A + A'

= 1

b) XY + XYZ' + XYZ' + XZY

= XY(1 + Z') + XY(Z' + Z)

= XY(1) + XY(1)

= XY + XY

= XY

Answer 2

$\huge\boxed{\boxed{\fcolorbox{white}{pink}{Answer}}}$

$\mathcal{1. AB+AB'+A'C+A'C'}$

$\mathcal{A(B+B')+A'(C+C')}$

$\mathcal{A+A'}$

$\mathcal{ 1}$

$\mathcal{ 2. XY+XYZ'+XYZ'+XYZ}$

$\mathcal{ XY(1+Z') + XY(Z'+Z)}$

$\mathcal{ XY+XY}$

$\mathcal{ XY}$

Hope it helps úh