duality

Question

Consider the circuit diagram given below

Given                f₁ = Σm (1, 2, 4, 6, 7)
                          f₂ = Σm (2, 3, 4, 5)
                          f₃ = Σm (0, 1, 2, 3)
                          f₄ = Σm (0, 2, 4, 6)
If the boolean function f_d is dual of f₄, then the boolean function ‘f’ is ____________.

• Σm (0, 1, 2, 3, 4, 5, 6, 7)
• Σm (0, 1, 2, 3, 6, 7)
• Σm (0, 1, 2, 3, 7)
• None of these

Answer 1

p = f1 XOR f2 = {1,3,5,6,7}
q= (p AND f3)' = {1,3}' = {0,2,4,5,6,7}

fd= dual of f4 =f4
f4' = {1,3,5,7}
r = q OR f4' = {0,1,2,3,4,5,6,7}

Comments

dual of f4 i.e fd = $\prod$M (1, 3, 5, 7)

fd' = $ \sum$m (1, 3, 5, 7)   Is it correct ?