State Distributive law and verify it using truth table.

 

Answer:

There are two Distributive laws:   

(i) A.(B+C) =(A.B) + (A.C)

(ii) A+(B.C) = (A+B).(A+C)

Proof:

(i)

A

B

C

B+C

A.(B+C)

A.B

A.C

(A.B)+(A.C)

0

0

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

1

0

1

0

0

0

0

0

1

1

1

0

0

0

0

1

0

0

0

0

0

0

0

1

0

1

1

1

0

1

1

1

1

0

1

1

1

0

1

1

1

1

1

1

1

1

1

(ii)

A

B

C

B.C

A+(B.C)

A+B

A+C

(A+B).(A+C)

0

0

0

0

0

0

0

0

0

0

1

0

0

0

1

0

0

1

0

0

0

1

0

0

0

1

1

1

1

1

1

1

1

0

0

0

1

1

1

1

1

0

1

0

1

1

1

1

1

1

0

0

1

1

1

1

1

1

1

1

1

1

1

1

 

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.