Sets

Let $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$. Write $A \cup B$.

With the same $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$, write $A \cap B$.

In the universe $U = \{1, 2, 3, 4, 5, 6, 7, 8\}$, write the complement $A^{c}$ of $A = \{1, 2, 3, 4\}$.

Which statements are true? (Choose all that apply.)

What is the cardinality $|\{a, b, a, c, b\}|$?

A café offers 3 drinks and 4 snacks. A combo is an ordered pair (drink, snack). If $D$ is the set of drinks and $S$ the set of snacks, how many elements does $D \times S$ have?

In a class, 14 students play football, 9 play chess, and 5 play both. How many play at least one of the two games?

Write a Python function is_subset(a, b) that returns True exactly when every element of the set a is an element of the set b. Don't use Python's built-in <= or issubset — loop over the elements instead.