Simplify the following expression using Boolean Rules

Question

𝑥 = !𝐴.!𝐵.!𝐶 + !𝐴.𝐵.𝐶 + 𝐴.𝐵.𝐶 + 𝐴.!𝐵.!𝐶 + 𝐴.!𝐵.𝐶

Answer 1

Karnaugh Map

A B C !A !B !C !A.!B.!C !A. B. C ABC A! B !C A !B C F(a,b,c)

0 0 0 1 1 1 1 1 0 1 1 0

0 0 1 1 1 0 1 1 1 1 1 1

0 1 0 1 0 1 1 1 1 1 0 0

0 1 1 1 0 0 1 1 1 1 1 1

1 0 0 0 1 1 1 0 1 1 1 0

1 0 1 0 1 0 1 1 1 0 1 0

1 1 0 0 0 1 1 1 1 1 1 1

1 1 1 0 0 0 0 1 1 1 1 0

C/AB | 00 01 10 11

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0 | 0 1 1 1

1 | 0 0 1 0

row 1 columns 01,10

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AB!C

column 10

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A !B C

row 1 columns 10,11

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A!BC

A B! C + A !B C