Question

Consider the Boolean function f = (a + bc)⋅(pq + r). Complement f' of function f is:
1. (a' + b'c') ⋅ (p'q' + r')
2. a'(b' + c') + (p' + q')r'
3. (a' + b'c') + (p'q' + r')
4. (a'b'c') + (p'q'r')

Answer 1

Correct Answer - Option 2 : a'(b' + c') + (p' + q')r'

By using Demorgan's law:

(A + B)' = A'.B' and (A.B)' = A' + B'

Boolean function f = (a + bc)⋅(pq + r).

f = (a + bc)⋅(pq + r)

f = ((a + bc)⋅(pq + r))'

f = (a + bc)' + (pq + r)'

f = a'.(bc)' + (pq)'.r'

f = a'.(b' + c') + (p' + q').r'

(a + bc). (pq + r) =  a'(b' + c') + (p' + q').r'

Therefore option 2 is correct.