Subject    : Mathematics[br]Education Unit  : Junior High School[br]Class/Semester  : VII/1[br]Material   : Set

[color=#0000ff][b]Basic Competencies[/b][/color][br][br]3.4 Describe sets, subsets, universal sets, empty set, set complement, and perform operations binary on sets using contextual problems[br]4.4 Solve contextual problems related to sets, subset, universal set, empty set, complement sets and binary operations on sets

[color=#0000ff][b]Indicators of Competence Achievement[/b][br][/color]3.4.1. Mention members and not members of the set[br]3.4.2. Presenting a set by mentioning its members[br]3.4.3. Presenting a set by writing down its properties[br]3.4.4. Presenting sets with set-builder notation[br]3.4.5. Draw a Venn diagram of a set[br]3.4.6. Reading a Venn diagram of a set[br]3.4.7. Expresses the intersection of two sets[br]3.4.8. Expresses the union of two sets[br]3.4.9. Express the complement of a set[br]3.4.10. Express the difference of two sets[br]4.4.1. Solve contextual problems related to Venn diagrams[br]4.4.2. Solve contextual problems related to the intersection of two sets[br]4.4.3. Solve contextual problems related to the union of two sets[br]4.4.4. Solve contextual problems related to the complement of a set[br]4.4.5. Solve contextual problems related to the difference of two sets

[b][color=#0000ff]Learning Objectives[br][/color][/b]1. Students can name members and not members of the set[br]2. Students can present sets in different forms[br]3. Students can perform and solve problems related to set operations

[b][color=#0000ff]Worksheet Instructions[/color][/b][br]1. Please pray first[br]2. Read and understand the worksheet instructions, learning objectives and problems contained in the worksheets[br]3. Answer each question properly and correctly in this worksheet![br]4. The time allotted to do this worksheet is 2x40 minutes![br]5. If something is not clear, you can ask the teacher![br]6. Summarize what you get from this student worksheet!

[color=#0000ff][b]Time Allocation: 2 x 40 minutes[/b][/color]

[b]A. Definition of Set[/b][br][br]The set is defined as a collection of certain objects that have a clear definition and are considered as a single entity.[br][br]Take a look at the following example:[br][br][list=1][*]The set of two-legged animals[/*][*]The set of natural numbers[/*][*]Nice collection of paintings[/*][*]Smart group of people[/*][/list]Can you tell the difference between what is a set and what isn't?[br][br]Examples 1 and 2 are sets, while examples 3 and 4 are not sets.[br][br]For those who are still confused, here's why….[br][br]In the example of 1 two-legged animal, we will have the same opinion about any animal with two legs, such as chickens, ducks, and birds. Everyone agrees that these animals have two legs? Definitely agree. Well, two-legged animals have a clear definition so that it is a set. For example 2 natural numbers also have a clear definition so that it is a set.[br][br]In the example of 3 good paintings and the example of 4 smart people, both do not have a clear definition. The words good and smart have different definitions for everyone, for example I think painting A is good but you don't necessarily think painting A is good right? Therefore, good painting and smart people are not a group.

[b]B. Set Presentation[br][br][/b]1. Expressed by mentioning its members (enumeration)[br][br]A set can be expressed by naming all its members written in curly braces. When the many members are very There are many, this way of registering is usually modified, which is marked with three dot (“…”) with the meaning “and so on following the pattern”.[br]Examples:[br]A = {3, 5, 7}[br]B = {2, 3, 5, 7}[br]C = {a, i, u, e, o}[br]D = {…, −3, −2, −1, 0, 1, 2, 3, …}[br][br]2. Expressed by writing down the characteristics of its members[br][br]A set can be expressed by mentioning the properties it has members[br][br]Examples:[br]A is the set of all odd numbers greater than 1 and less than 8.[br]B is the set of all prime numbers less than 10.[br]C is the set of all vowels in the Latin alphabet.[br]D is the set of integers.[br][br]3. Expressed with set-builder notation[br][br]A set can be expressed by writing the membership conditions the set. This notation is usually of the general form {x | P(x)} where x represents the members of the set, and P(x) represents the conditions that must be[br]fulfilled by x in order to be a member of the set. x symbol can replaced by other variables, such as y, z, and others. For example A = {1, 2, 3, 4, 5} can be expressed with set-forming notation A = {x | x < 6, and x original}.[br]Coat of arms {x | x < 6, and x original} this can be read as “The set x such that x is less than 6 and x is an element of natural numbers}. However, if we understand well, then this symbol is usually simply read with "The set of natural numbers less than 6".[br][br]Examples:[br]A = {x | 1 < x < 8, x is an odd number},[br](read: A is the set whose elements are all x such that x is greater than 1 and x is less than 8, and x is an odd number).[br]B = {y | y < 10, y is a prime number}.[br]C = {z | z is a vowel in the Latin alphabet}.

[b]C. Venn Diagram[/b][br][br]How to present the set can also be expressed with pictures or diagrams this is called a Venn Diagram. Venn diagram introduced by expert English mathematician John Venn (1834 – 1923). Instructions in[br]create a Venn diagram include:[br][list=1][*]The universal set (S) is represented as a rectangle and the letter S placed in the upper left corner.[/*][*]Every set in the universal set is represented by simple closed curve.[/*][*]Each member of the set is indicated by a dot.[/*][*]If the members of a set have many members, then the members do not need to be written down[/*][/list][br][br]Observe the Venn diagram presentation of the following example.[br][list=1][*]Venn diagram of the set S ={1, 2, 3, 4, 5, 6, 7, 8, 9}, the set A = {1, 2, 3} and the set B ={ 4, 5, 6} are as follows.[/*][/list]

2. Venn diagram of the set S ={1, 2, 3, 4, 5, 6, 7, 8, 9}, the set A ={1, 2, 3, 4}, the set B ={ 4, 5, 6, 7} is as follows.

[b]D. Set Operations[br][br][/b]So far you are familiar with operations in numbers. Just like numbers, sets can also be interoperable with each other. Operations the set includes:[br][list=1][*]Intersection[/*][*]Union[/*][*]Difference[/*][*]Complement[/*][/list][br]1. Intersection[br][br]The intersection of two sets A and B is the set of all members of the same sets A and B. In other words, the set whose members are in both sets.[br][br]Example: A = {a, b, c, d, e} and B = {a, c, e, g, i}[br][br]The two sets have three members in common, namely a, c, and e. Therefore, it can be said that the intersections of sets A and B are a, c, and e or written as:[br][math]A\cap B[/math] = {a, c, e}[br][br][math]A\cap B[/math] is read as set A, the intersection of set B.[br][br]2. Union[br][br]The union of two sets A and B is a set that consists of all the members of a set A and a set B, where the same member is only written once.[br][br]A combined B is written [math]A\cup B[/math] = {x|x A or x B}[br][br]Example:[br]A = {1, 2, 3, 4, 5}[br]B = {2, 4, 6, 8, 10}[br][math]A\cup B[/math] = {1, 2, 3, 4, 5, 6, 8, 10}[br][br]3. Difference[br][br]The difference between two sets A and B is the set of all members of set A but not set B.[br][br]A difference in B is written A-B = {x|x A or x B}[br][br]Example:[br]A = {a, b, c, d, e}[br]B = {a, c, e, g, i}[br]A-B = {b,d}[br][br]4. Complement[br][br]The complement of A is the set of all elements of S that are not in the set A.[br][br]A's complement is written [math]A\begin{matrix}'\end{matrix}[/math] or [math]A^c[/math] = {x|x S or x A}[br]Example:[br]A= {1, 3, …, 9}[br]S = {an odd number less than 20}[br][math]A^c[/math] = {11, 13, 15, 17, 19}

After studying the materials above, the following is a learning video that students can watch. This video aims to strengthen material on the concept of sets, how to present sets, and set operations

EXERCISE

[i]For questions number 4-8 pay attention to the following geogebra. Students can click on the boxes provided to find out the answers.[/i]