State and verify Absorption law algebraically.

 

Answer:

Absorption law states that:

  • A.(A+B) = A
  • A+(A.B) = A

Algebraic Method for verification:

  1. LHS = A.(A+B)                               

        = A.A + A.B                                     (using Distributive law)

        = A + A.B                                        (using Idempotent law)

        = A.(1+B)                                        (using Distributive law)

        = A.1                                               (using Annulment law)

        = A                                                  (using Identity law)

        = RHS

  • LHS = A+(A.B)

        = (A.1) + (A.B)                                (using Identity law)

        = A.(1+B)                                        (using Distributive law)

        = A.1                                               (using Annulment law)

        = A                                                  (using Identity law)

        = RHS

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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.