The Lumenary · 3.º a 5.º grado

Sets

Nombre: ______________________

Fecha: ______________________

Aprenderás a

1.
Let $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$ . Write $A \cup B$ .
2.
With the same $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$ , write $A \cap B$ .
3.
In the universe $U = \{1, 2, 3, 4, 5, 6, 7, 8\}$ , write the complement $A^{c}$ of $A = \{1, 2, 3, 4\}$ .
4.
Which statements are true? (Choose all that apply.)
- A. $3 \in \{1, 2, 3\}$
- B. $\{3\} \subseteq \{1, 2, 3\}$
- C. $\{3\} \in \{1, 2, 3\}$
- D. $\varnothing \subseteq \{1, 2, 3\}$
5.
What is the cardinality $|\{a, b, a, c, b\}|$ ?
6.
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?
7.
In a class, 14 students play football, 9 play chess, and 5 play both. How many play at least one of the two games?
8.
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.
Computacional — Práctica

Solucionario — Sets

1.
Everything in $A$ or $B$ : $A \cup B = \{1, 2, 3, 4, 5, 6\}$ . The shared elements $3$ and $4$ are listed once, because sets ignore repetition.
2.
Only $3$ and $4$ are in both, so $A \cap B = \{3, 4\}$ .
3.
$A^{c} = U \setminus A = \{5, 6, 7, 8\}$ . If the universe were different, the complement would be different too.
4.
The true statements are $3 \in \{1,2,3\}$ , $\{3\} \subseteq \{1,2,3\}$ and $\varnothing \subseteq \{1,2,3\}$ . The statement $\{3\} \in \{1,2,3\}$ is false: the elements are the numbers $1, 2, 3$ , not the set $\{3\}$ . The empty set is a subset of everything because it has no element that could fail to belong.
5.
Without repeats the set is $\{a, b, c\}$ , so its cardinality is $3$ .
6.
Each of the 3 drinks pairs with each of the 4 snacks, giving $|D \times S| = |D| \cdot |S| = 3 \cdot 4 = 12$ ordered pairs.
7.
$|A \cup B| = 14 + 9 - 5 = 18$ . Adding $14 + 9$ counts the 5 students in the overlap twice, so we subtract them once.
8.
Follow the definition: check each element of a.
```
def is_subset(a, b):
    for x in a:
        if x not in b:
            return False
    return True
```
Notice the empty set: the loop runs zero times, so the function returns True — exactly matching the mathematical fact that $\varnothing \subseteq B$ for every $B$ .