How to solve for QTy B? Can You please Explain?

There are 180 customers in total.
- 90 customers purchased zucchini.
- 115 customers purchased cauliflower.

Let:
- $Z=$ the set of customers who purchased zucchini.
- $C=$ the set of customers who purchased cauliflower.
- $x=$ the number of customers who purchased both zucchini and cauliflower.

Using the principle of inclusion-exclusion:

$$
\(\begin{gathered}
|Z \cup C|=|Z|+|C|-|Z \cap C| \\
|Z \cup C|=90+115-x=205-x
\end{gathered}\)
$$


Since there are 180 customers total, the number purchasing neither zucchini nor cauliflower is:

$$
\(180-|Z \cup C|=180-(205-x)=x-25\)
$$


Quantity A is the number who purchased both zucchini and cauliflower: $x$.
Quantity $B$ is the number who purchased neither: $x-25$.
Since the number of customers cannot be negative, $x$ must be at least 25 to have a valid number for "neither" customers.

Comparing Quantity A and Quantity B:

$$
\(x \quad \text { vs } \quad x-25\)
$$


Clearly,

$$
\(x>x-25\)
$$