Check sibling questions

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) .

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.