How can I compute the complement of a mathematical membership function?

Question

Considering fuzzy set A defined on real numbers by the membership functions:

$\mu_A(x)=\frac{1}{x+1}, \mu_C(x)=\frac{1}{10^x}$

How can I determine mathematical membership function and graph of $ A \cap \overline{C}$ ?

Till know I have tried the above :

Let A be a fuzzy set in the universe of information say U. Then, A can be defined as a set of ordered pairs represented mathematically as $A = \{(g,\mu_A(g)): g \in U\}$ where $\mu_A(g)$ is the degree of membership of $g$. Also, the range for the membership function is $\mu_A \in [0,1]$ .

$ A \cap \overline{C}$ = {(g,$\mu_{A \cap \overline{C}}(g)): g \in$ U}

I am stuck on how I can compute the complement of $C \equiv\overline{C}$ ?

Considering $A \cap \overline{C} = \{(g,min(\mu_A(g), 1-\mu_C(g)) : g \in$ U }

How can I represent this set graphically ?

Answer 1

$A \cap \overline{C} = \{(g,min(\mu_A(g), 1-\mu_C(g))) : g \in U \}$