State and verify Absorption law algebraically.
Answer:
Absorption law states that:
- A.(A+B) = A
- A+(A.B) = A
Algebraic Method for verification:
- 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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