Question

Simplify the following expression Y = (A + B)(A + C' )(B' + C' )

Answer 1

Step-by-step explanation:

Y = (A+B)(A+C′)(B′+C′)

=(AA+AC′+AB+BC′)(B′+C′)

=(A+AC′+AB+BC′)(B′+C′)

=(A(1+C′+B)+BC′)(B′+C′)

=(A+BC′)(B′+C′)

=AB′+AC′+B′BC′+BC′C′

=AB′+AC′+0+BC′

=AB′+AC′+BC′

Answer 2

Y =  (A + B)(A + C' )(B' + C' )  = AB' + AC' +  BC'

Given:

• Y = (A + B)(A + C')(B' + C')

To Find:

• Simplify the expression

Solution:

• X + X' = 1
• X + 1  = X
• X.X'  = 0
• X. X = X
• X'.X' = X'
• X + X  =X
• X' + X' = X'
• X. 1 = X

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

Product of First two brackets

Y = (AA + AC' + BA  + BC')(B' + C')

Use AA = A

Y =  (A + AC' + BA  + BC')(B' + C')

Use A = A.1

Y = (A.1 + AC' + BA + BC')(B' + C')

Take A common

Y = (A(1 + C' + B)  + BC') (B' + C')

Use 1 + C' + B  = 1

Y = (A.1 + BC')(B' + C')

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

Take Product

Y = AB' + AC' + BC'B'  + BC'C'

Y = AB' + AC' + C'BB'  + BC'C'

Use BB'  = 0    and C'C' = C'

Y = AB' + AC' + C'.0 + BC'

Use C'.0 = 0

Y = AB' + AC' +  0 + BC'

Y = AB' + AC' +  BC'

Hence (A + B)(A + C' )(B' + C' )  = AB' + AC' +  BC'