State and verify the associative law using the Truth table.

 

Answer:

Associative law states that:  

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

Proving using truth table:

A

B

C

(A+B)

(A+B)+C

(B+C)

A+(B+C)

0

0

0

0

0

0

0

0

0

1

0

1

1

1

0

1

0

1

1

1

1

0

1

1

1

1

1

1

1

0

0

1

1

0

1

1

0

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

1

1

1

1

Hence, from the truth table, we have proved that (A+B)+C = A+(B+C) .

A

B

C

(A.B)

(A.B).C

(B.C)

A.(B.C)

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

1

0

0

0

0

0

0

1

1

0

0

1

0

1

0

0

0

0

0

0

1

0

1

0

0

0

0

1

1

0

1

0

0

0

1

1

1

1

1

1

1

Hence, from the truth table, we have proved that (A.B).C = A.(B.C) .

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.