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ACtE08 · Chapter 8Mock Test 02🏛️ Past Licensure QuestionID: f248089d

The Boolean expression A + BC is the reduced form of:

Multiple Choice Options

A
AB + BC
B
(A + B)(A + C)
✓ Correct Option
C
(A + C)B
D
(A + B)C

Detailed Technical Solution & Explanation

By applying the second distributive law of Boolean algebra ( $X + YZ = (X + Y)(X + Z)$ ):

(A + B)(A + C) = A \cdot A + AC + AB + BC

Since $A \cdot A = A$ :

= A + AC + AB + BC

Factoring $A$ :

= A(1 + C + B) + BC

Since $(1 + \text{anything}) = 1$ :

= A(1) + BC = A + BC

Thus, $A + BC$ is the minimal/reduced form of $(A + B)(A + C)$ .

Option Analysis:

•

Option A (AB + BC): Incorrect; factors to

B(A + C)

, which is not equivalent to

A + BC

•

Option B ((A + B)(A + C)): Correct; expands directly to

A + BC

by Boolean distribution.

•

Option C ((A + C)B): Incorrect; expands to

AB + BC

•

Option D ((A + B)C): Incorrect; expands to

AC + BC

Reference: Mock Test 02NEC Licensure Syllabus

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