📘 set theory

1. **State the problem:** We have a universal set $U$ with $n(U) = 100$ elements and two subsets $A$ and $B$ with $n(A) = 20$, $n(B) = 60$, and their intersection $n(A \cap B) = 10

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 $n(A \cap B) = 10$.

1. **State the problem:** We are given a universal set $U$ with two subsets $A$ and $B$ represented in a Venn diagram. The numbers in each region are: - $A$ only: 34

1. The problem asks for the number of elements in the union of sets A and B, denoted as $n(A \cup B)$. This means we want to find how many elements are in either set A, set B, or b

1. **State the problem:** Given the universal set $U = \{6, 7, 8, 9, 10, 11, 12\}$ and subset $A = \{9, 10, 11, 12\}$, find the complement of $A$, denoted $A'$. 2. **Recall the def

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 $B=\{3,4,5\}$.