$5$

Consider a school with two periods during which

classes can be scheduled. For each class, there are

two variables. For example, for class $A,$ there are

variables $x_{A1}$ and $x_{A2}.$ Setting $x_{A2}=1$

represents scheduling class A during period $2.$

Select the Boolean expression that is true if and

only if classes A and $B$ are not scheduled during

the same period.

$(\frac{?}{\text{b}\text{a}\text{r}}(x_{A1}+x_{A2}))(\frac{?}{\text{b}\text{a}\text{r}}(x_{B1}+x_{B2}))$

$(\frac{?}{\text{b}\text{a}\text{r}}(x_{A1}{x}_{B1}))(\frac{?}{\text{b}\text{a}\text{r}}(x_{A2}{x}_{B2}))$

$(\frac{?}{\text{b}\text{a}\text{r}}(x_{A1}+x_{B1}))(\frac{?}{\text{b}\text{a}\text{r}}(x_{A2}+x_{B2}))$

$(\frac{?}{\text{b}\text{a}\text{r}}(x_{A1}{x}_{A2}))(\frac{?}{\text{b}\text{a}\text{r}}(x_{B1}{x}_{B2}))$