UNIVERSE SET: Formulas and Example Problems

July 06, 2022
InMiscellanea

Have you ever grouped equations of many units into the same unit? If so, it can be said that it is included in the universal set. This set itself is one of 4 types of sets that can be found in mathematics lessons.

You could say this type of set is the easiest type of set to operate. The result of the set cannot be written arbitrarily. You need to know how to write it so that the final answer is not declared wrong.

One of the 4 types of sets in mathematics, the set itself is a collection of objects that are declared similar and are considered as a unit.

List of contents

Definition of the Universal Set

The universal set or many called the universal set is a type of set that contains objects that can be said to be similar. All set objects or their members are categorized as a single unit.

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This type of set has only one letter symbol, namely 'S'. Of course, just like other types of sets, this type of set has its own way of writing. Don't get me wrong, you need to know how to write it properly.

For example, the group X = {red, white, blue, yellow, gray} then if we use the concept of the universal set it will be S = {color type}. In practice, you will find questions about the combined object of the universe with the root of the problem finding the concept of the universe.

Read: Math Circle

Types of Universal Sets

Actually the set of this type does not have a division of types anymore in it. Therefore this information is often used to deceive. So make no mistake that this set has absolutely no division of types in it.

The concept that is owned is only one, namely looking for a universal set of various types of objects even to dissimilar objects. Usually when it is necessary and directed to determine the results in the form of a diagram, the Venn diagram will be used later.

Read: Permutations and Combinations

The formula for declaring a set

Of course, sets of this type have their own way of asserting the object of the set. The formula for declaring a set is quite easy to remember. First, let's look at a brief description of the symbols that will be used in this universal set.

1. S

The first symbol is the capital letter 'S' which is the symbol of the word universal or universe. It's easy enough to remember because the symbol is the first letter of the name of the set to be used.

2. {…, …., …}

The symbol above is a type of bracketed writing symbol. This symbol will also always be used when you want to write down the results of working with the universal set method. Before and after the mention of results must be accompanied by brackets of this type and cannot be bracketed by other types.

From the two symbols above, the formula for writing the universal set will appear. Both symbols will always be there when you work on problems related to sets. The main writing formula for the universal set type is:

S = {…, …., …}

With the dots in the contents of the searched universe object results. Contents can be in curly brackets and can be very long or short depending on the questions given. Don't forget to use a comma (,) if there is more than one object as a separator for the description of the object you get.

Read: Mathematical Set

Examples of Universal Set Problems and Discussion

The more often you study sample questions, the more likely you are to get used to mastering this type of material. To better understand or use it as training material, you can see the example below:

Example Question 1

The following sets are known:

V = {-9. -12, -14, -16, -17, -20, -23, -25, -26}

X = {yacht, helicopter, motorcycle, truck, bus, train, car}

Y= {kiwi, rambutan, melon, avocado, watermelon, pineapple, plum}

Z = {1, 3, 5, 7, 11, 13, 17, 19, 23, 27}

Determine the universal set from each of the above sets!

Answer:

V = {set of negative integers}

X = {transport set}

Y = {set of various types of fruit}

Z = {set of prime numbers}

Example Question 2

Find the various possible universal sets of the set W = {7, 11, 13, 17, 19, 23, 27, 29, 31, 37}.

Answer:
There are at least 5 kinds of possible universe sets that are possible from these sets. Among them:

S = {7, 11, 13, 17, 19, 23, 27, 29, 31, 37}
S = {prime number}
S = {odd number}
S = {part of whole number}
S = {part of real number}

Example Question 3

A random set is represented by:

A = {horse, cat, rabbit}

B = {whale, dolphin, seal, walrus}

C = {square, triangle, parallelogram, rectangle}

D = {cube, cuboid, cone, triangular prism, hexagon prism}

Determine the possible universal set of each set.

Answer:

– Set A:

S = {animal group}

S = {a group of four-legged animals}

S = {a group of mammals}

– Set B:

S = {the set of animals that spend most of their time in water}

S = {set of aquatic mammals}

S = {set of legless animals}

– Set C:

S = {flat up}

S = {cornered flat shape}

– Set D:

S = {set of shapes}

S = {set of geometric shapes}

S = {set of angular shapes}

Example Question 4

Determine at least two universal sets from each of the following sets:

E = {lemon yellow, mandarin orange, pink, turquoise}

U = {blender, speaker, charger}

I = {pens, markers, crayons}

O = {12, 24, 48, 96}

Answer:

– E set

S = {set of light colors}

S = {set of child colors}

– U. set

S = {everyday electronic device}

S = {electronic device with a transformer element in it}

– Set I

S = {office stationery (ATK)}

S = {stationery that cannot be erased by ordinary rubber erasers}

– O set

S = {set of real numbers}

S = {set of even numbers}

S = {set of numbers that are multiples of 12}

S = {set of numbers that are divisible by 4, 6, and 12}

Example Question 5

From a single set F = { farmer, singer, banker, crew, engineer, accountant, secretary, writer, painter, photographer, stylist stage, comedian, swordsman, fisherman, pilot, shoemaker, athlete, president}, determine the universal set that is most likely to form.

Answer:

S = {set of types of work}

Example Question 6

From the universal set S = {name of city in Indonesia} mention 3 examples of sets that might be included in it.

Answer:

Cities in West Java = {Bandung, Bogor, Ciamis, Garut, Bekasi, Cianjur}

Cities in Central Java = {Semarang, Kudus, Salatiga}

City in North Kalimantan = {Tarakan}

Example Question 7

From the universal set S = {name of stringed instrument} state what are examples of sets that might be included in it:

Answer:

Q = {guitar, ukulele, sasando, harp, harp, trumpet, sinter}

There are many other types of questions that you can practice at home. You can also try creating your own set type. Don't forget to use braces, not any other type of parenthesis, to define the discovery of the universal set.

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