Computer Science

Simplify a.b + a'.c + b.c using the laws of boolean algebra. At each step, state clearly the law used for simplification.

Boolean Algebra

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  a.b + a'.c + b.c
= a.b + a'.c + b.c(a + a')      [Complementary Law: A+A'=1]
= a.b + a'.c + a.b.c + a'.b.c   [Distributive Law]
= a.b + a.b.c + a'.c + a'.b.c   [Associative Law]
= a.b + a'.c                    [Absorbtion Law]

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Computer Science

Simplify a.b + a'.c + b.c using the laws of boolean algebra. At each step, state clearly the law used for simplification.

Boolean Algebra

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