CSE370 Quiz 1 Solution


1. Write down a Boolean expression corresponding to the following logic circuit. Fill in the truth table for the function.

Note that A' + B + C' is a maxterm (0 for the case when A=1, B=0, and C=1, and 1 otherwise).

A
B
C
F
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1

2. Prove that the following is true using the axioms/theorems of Boolean algebra (show each step of your proof):

(A + B) (A + BC)
=
(A + BC)
A(A + BC) + B(A + BC)
=
A + BCdistributivity
AA + ABC + AB + BBC
=
A + BCdistributivity
A + ABC + AB + BC
=
A + BCidempotency
A(1 + BC + B) + BC
=
A + BCdistributivity
A(1) + BC
=
A + BCidentity
A + BC
=
A + BCidentity
Done

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