📘 set theory

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

1. The problem is to explain **"A and B" for sets** with a simple example, not a general rule. 2. For sets, **"A and B"** usually means the **intersection**, written as $A\cap B$.

1. The problem is asking about the same example, but using $a$ or $b$ for sets. 2. A simple example is:

1. The problem is to draw and explain sets $A$ and $B$ with an example, not in a general way. 2. Let’s use a simple example with numbers:

1. The problem asks to draw and, for sets like $A$ and $B$, show the relationship between them. 2. A standard way to represent sets is with a Venn diagram.

1. The problem is to draw a diagram for the union of sets. 2. For two sets $A$ and $B$, the union is written as $A \cup B$.

1. **Stating the problem:** We are given classes and relations with specific properties and asked: Given that $M$ and $N$ belong to $\mathrm{Sel}(P,A)$, $M \neq N$, and condition (

1. **Stating the problem:** We want to find elements $x,y$ such that $xR!y$ holds but $xR^*y$ does not. 2. **Recall definitions:**

1. **State the problem:** We need to shade the sets $X \cap (Y \cup Z)$ and $(X \cap Y) \cup (X \cap Z)$ in Venn diagrams and then conclude the relationship between these two sets.

1. **State the problem:** We have a universal set $S = \{1, 2, 3, \ldots, 20\}$ and two subsets:

1. **State the problem:** We are given two sets $A$ and $B$ which are subsets of the universal set $S = \{1,2,3,\ldots,20\}$. We need to find the union $A \cup B$ and the intersect