Reference no: EM131385705
1. Construct a truth table for the following:
a) yz + z(xy)'
b) x(y'+z) + xyz
c) (x + y)(x' + y)
2. Use only the first seven Boolean identities to prove the Absorption Laws.
3. Show that x = xy + xy'
a) Using truth tables
b) Using Boolean identities
4. Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step.
a) F(x,y,z) = y(x' + (x + y)')
b) F(x,y,z) = x'yz + xz
c) F(x,y,z) = (x' + y + z')' + xy'z' + yz + xyz
5. Using the basic identities of Boolean algebra, show that:
x + x' y = x + y
6. The truth table for a Boolean expression is shown below. Write the Boolean expression in sum-of-products form.
x y z F
0 0 0 1
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 0
1 1 1 0
7. Draw the truth table and rewrite the expression below in product-of-sums form:
xy' + x'y +xz + y'z
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