A self-dual logic function is a function F such that F = FD. Which of the following functions are self-dual? (Here, ⊕ denotes the Exclusive OR (XOR) operation.)
(a) F = X
(b) F = X,Y,Z(1, 2, 5, 7)
(c) F = X′ ⋅ Y ⋅ Z′ + X ⋅ Y′ ⋅ Z′ + X ⋅ Y
(d) F = W ⋅ (X⊕Y⊕Z⊕W′) + (X⊕Y⊕Z)
(e) A function F of 6 variables such that F = 1 if and only if 3 or more of the variables are 1
(f) A function F of 9 variables such that F = 1 if and only if 5 or more of the variables are 1
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