Answer Happy

1. Recall a variable 𝑥 is in the support of 𝑓 if there are 𝑦, 𝑧,
... so that 𝑓(1, 𝑦, 𝑧, ... )
is not equal to 𝑓(0, 𝑦, 𝑧, ... )
a) Write an 𝑓 in sum of products form where the variable 𝑥
appears
explicitly in some of the products, but 𝑥 is not in the support of
𝑓
b) How many functions 𝑓(𝑥, 𝑦, 𝑧) of 3 variables exist such that all
three
variables are in the support of 𝑓 ?
Hint: start counting functions with 0 variable support, 1 variable,
... etc.
Then note we can extend functions in two variables to three in
three
ways, picking as the supporting variables the pairs (𝑥, 𝑦),(𝑥, 𝑧),
(𝑦, 𝑧).