📘 set theory

1. **State the problem:** Find the intersection of the sets $\{2, 9\}$ and $\{1, 4, 9\}$. This means we want to find all elements that are in both sets. 2. **Recall the definition

1. **State the problem:** We have a class of 30 music students. Among them, 13 play the piano, 16 play the guitar, and 6 play both instruments. We need to find how many students pl

1. The problem asks which of the numbers $x$, $y$, $z$, or $w$ must equal 0 if $A \cup B = U$. 2. Recall that $A \cup B = U$ means the union of sets $A$ and $B$ covers the entire u

1. **State the problem:** We are given the number of elements in complements and unions of sets A and B, and we need to find the number of elements in each of the four regions of t

1. **State the problem:** We are given the cardinalities of complements and unions of sets and need to find the number of elements in the set $n(A \cap B)$. 2. **Given:**

1. **State the problem:** We are given the sizes of complements and unions of sets and need to find $n(A \cap B')$. 2. **Given:**

1. **State the problem:** We are given two sets $A$ and $B$ with the following information: - $n(A) = 30$

1. **State the problem:** We are given the sizes of sets $A$, $B$, their union $A \cup B$, and the universal set $U$. We need to find the number of elements in the subset $A \cap B

1. **State the problem:** We are given a universal set $U$ with $n(U) = 100$, and two subsets $A$ and $B$ with $n(A) = 20$, $n(B) = 60$, and their intersection $n(A \cap B) = 5$. W

1. **State the problem:** We have 100 people surveyed about desserts. - 55 had cake.

1. **State the problem:** Find the complement of set $A=\{1,3,5,7\}$ with respect to the universal set $U=\{1,2,3,4,5,6,7\}$. 2. **Recall the definition:** The complement of $A$ wi

1. **Problem statement:** In a class of 50 students, 20 are certified in Java, 15 are certified in SQL, and 5 are certified in both Java and SQL. We need to find how many students

1. **Problem:** Draw a Venn diagram for a set union with an example. 2. **Rule for union:** The union of two sets, written as $A \cup B$, includes everything that is in $A$, in $B$

1. **Problem:** Draw $A$ or $B$ as a diagram. 2. **Formula used:** In set notation, “or” means the union, written as $A\cup B$.

1. **Problem:** Draw **$A$ or $B$**. 2. **Formula used:** In set notation, **“or”** means the **union**: $$A\cup B$$.

1. **Problem:** Draw the example sets $A$ and $B$. 2. **Example sets:** Let $A=\{1,2,3\}$ and $B=\{3,4,5\}$.

1. **Problem:** Draw and explain sets like $A$ or $B$ with an example, not in general scope. 2. **Example sets:** Let $A=\{1,2,3\}$ and $B=\{3,4,5\}$.

1. Problem: draw the sets example for $a$ and $b$. 2. Use one concrete example: $a=\{1,2,3\}$ and $b=\{3,4\}$.

1. Problem: draw and, for sets like $a$ or $b$, give an example instead of a general explanation. 2. This is a request for a simple set example, so we can use two sets and show one

1. The problem is to draw and provide examples of sets like \(A\) or \(B\) with specific elements, not just general descriptions. 2. A set is a collection of distinct objects, call

1. **Problem statement:** Draw an example of sets $A$ and $B$. 2. A simple example is to use two overlapping sets so you can see elements that are only in $A$, only in $B$, and in