# Set theory: Problem 1

### Solution

$$A \times (B\cup C) = A \times \{3, 4, 8\} =$$ {(green, 3), (green, 4), (green, 8), (red, 3), (red, 4), (red, 8)}

$$B\cap C = \{8\}$$

{camel}$$\times (B\cap C) =$${camel} $$\times$$ {8} = {(camel, 8)}

$$A \cap C = \emptyset$$

### Self-check

Did you make the correct choice of parentheses vs. curly brackets? Parentheses enclose ordered pairs, whereas curly brackes enclose sets.

In the first answer, the order of the items in each pair matters, e.g. (3, green) would be wrong. However, it doesn't matter what order you list the pairs in.

Did you have exactly six pairs? Notice that there must be six pairs, because A contains 2 elements and $$B \cup C$$ contains 3.

In the second formula, notice that the intersection operation takes sets as inputs and returns a set as output. So the answer must be {8} (a set), not 8 (a number).

In the third answer, the output should be a set of ordered pairs. Did you write both the parentheses and the curly brackets?

In the last formula, did you use the correct notation $$\emptyset$$ for the empty set? Writing {} seems logical, and it might work in some programming languages, but it is not literate mathematics.