You didn't write the questions you need to be solved with the information you gave.
The problem is under SET, and I will explain the topic, using the information you gave.
SET
A Set is any well-defined collection of objects. These objects could be people’s names, their ages, hubbies, dislikes; etc
These objects must be related through the same rule.
For example:
- A group of possible outcomes of a dice roll;
- A group of possible outcomes of a coin toss;
- Set of all whole numbers;
- Set of all prime numbers;
- Set of all even numbers;
- Set of all odd numbers;
- A collection of students with a CGPA of 4.0.
And so on.
There should be a universal rule that defines law through which we collect or group objects.
For example, "a group of all the talented musicians" is not well-defined, as the musicians I refer to as "talented", might be different from yours, it will have different names inside it.
Conventions that are used here:
- Sets are usually denoted by a capital letter.
- The elements of the group are usually represented by small letters (unless specified separately.)
- If ‘a’ is an element of ‘A’, or if a “belongs to” A, it is written as a ϵ A.
- If b is not an element of Set A, b “does not belong to” A is written in the conventional notion by the use of the symbol Epsilon with a line across it) between them.
- Elements, entities, members, objects, all mean the same thing.
REPRESENTATION OF A SET
Representation of a set and its elements is done in the following two ways.
(1) ROSTER FORM
In this form, all the elements are enclosed within curly brackets {} and they are separated by commas (,).
The order in which the elements are listed in the Roster form for any Set is immaterial. For example, T = {v, w, x, y, z} is same as T = {z, y, x, w, v}.
The dots at the end of the last element of any Set represent its infinite form and indefinite nature. For example, group of odd natural numbers = {1, 3, 5, …}
Elements of a set in this form are generally not repeated. For example, the set of alphabets forming the word FOOD = {F, O, D}
More examples for Roster form of representation are:
A = {2, 4, 8, 16}
B = {3, 9, 27, 81, 243}
C = {1, 4, 9, 16, …, 100}
(2) SET BUILDER FORM
In this form, all the elements possess a single common property which is not featured by any other element outside the Set. For example, a group of consonants in English alphabetical series.
The representation is done as follows.
Let C be the collection of all English consonants, then – V = {x: x is a consonant in English alphabetical series.}.
Colon (:) is a mandatory symbol for this type of representation.
After the colon sign, we write the common characteristic property possessed by all the elements belonging to that Set and enclose it within curly brackets.
If the Set doesn’t follow a pattern, its Set builder form cannot be written.
More examples for Set builder form of representation for a Set:
M = {y: y is an integer and – 9 < y < 20}
P = {x: x is a whole number less than 7}
X = {n: n is a negative integer > -10}
And so on.
Operations on Sets using the Sets you gave.
Given that
U = {1 , 2 , 3 , ... , 18 , 19 , 20}
A = {4 , 5 , 7 , 8 , 15 , 19 , 20}
B = {1 , 2 , 3 , 4 , 5 , 6 , 8 , 9 , 10 , 13 , 15 , 16 , 18 , 19}
C = {1 , 3 , 5 , 7 , 9 , 10 , 11 , 15 , 18 , 20}
- UNIVERSAL SET is the Set U, in which every elements in SUBSETS A, B, and C are found.
- COMPLEMENT of the set A is the set of elements that are not found in A, but are U. It is written as
A' = {1, 2, 3, 6, 9, 10, 11, 12, 13, 14, 16, 17, 18}
- UNION of sets A and C is the set that contains every element in A and C. If an element appears in both A and C, we only write it once. It is written as
A U C = {1, 3, 4, 5, 7, 8, 9, 10, 11, 15, 18, 19, 20}
- INTERSECTION of sets A, B, and C is the set of elements that are common to A, B, and C. It is written as
A n B n C = {5, 15}
- EMPTY SET is a set that contains no element in it. It is written as Φ (Greek letter, phi), or {}, but not as {Φ}.
Example A n A' = {}
