Question

Using the algebraic manipulation, Simplify the following expression

Y = (A + B)(A + C' )(B' + C' )

Answer 1

• First expand (A+B)(A+C') using distributive law
• (A+B)(A+C') =AA+AC'+BA+BC'=A+AC'+BA+BC' (Idempotent law AA=A)
• Then (A + B)(A + C')(B' + C')=(B' + C')(A+AC'+BA+BC')
• Expanding(B' + C')(A+AC'+BA+BC') using distributive law
• (B' + C')(A+AC'+BA+BC')=B'A+B'AC'+B'BA+B'BC'+C'A+C'AC'+C'BA+C'BC'
• =B'A+B'AC'+C'A+C'A+C'BA+C'B(By applying BB'=0(Complementary law) and C'C'=C'(Idempotent law AA=A)
• =B'A+B'AC'+C'A+C'BA+C'B (Applying C'A+C'A=C'A(Idempotent law))
• =B'A(1+C')+C'A(1+B)+C'B (Taking B'A and C'A outside)
• =B'A+C'A+C'B (By applying additive identity A+1=1
• =AB'+AC'+BC'
• Y=(A+B)(A+C')(B'+C')=AB'+AC'+BC'