• A set is a collection of well-defined objects or elements. 

  • When we say a set is well-defined, we mean that if an object is given, we are able to determine whether the object is in the set or not.

i) Sets are usually denoted by capital letters like 𝐴, 𝐵, 𝐶, 𝑋, 𝑌, 𝑍, etc.

ii) The elements of a set are represented by small letters like 𝑎, 𝑏, 𝑐, 𝑥, 𝑦, 𝑧, etc.

If 𝑎 is an element of set 𝐴, we say “𝑎 belongs to 𝐴”, we write 𝒂 ∈ 𝑨 and we read as “𝒂  is a member of A”.

If 𝑏 is not an element of set 𝐴, we write 𝒃 ∉ 𝑨 and read as “𝑏 does not belong to set 𝐴” or “𝑏 is not a member of set A”.

                                       

a. The set of students in your class is a well-defined set since the elements of the set are clearly known. 

b. The collection of kind students in your school. This is not a well-defined set because it is difficult to list members of the set.

c. Consider 𝐺 as a set of vowel letters in English alphabet. Then 𝑎 ∈ 𝐺, 𝑜 ∈ 𝐺, 𝑖 ∈ 𝐺, but 𝑏 ∉ 𝐺.

Suppose that A is the set of odd natural numbers. Write the symbol ∈ or ∉ in the blank spaces.

A.   3_____ A 

B.   5_____ A 

C.  -6_____ A

D.   4____ A

1. Which of the following is a well-defined set? Justify your answer.

a. A collection of all boys in your class.

It is well-defined set

b. A collection of efficient doctors in Black Lion Hospital.

It is not well-defined set

c. A collection of all natural numbers less than 100.

It is  well-defined set

d. The collection of songs by Artist Tilahun Gessesse.

It is well-defined set

e. Collection of beautiful girls in your class.

It is not well-defined set

f. Collection of consonants of the English alphabet.

It is  well-defined set

2. Let 𝐴 = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces:

a.     5 ____ A

b.     8 ____ A

c.   0____A

d.    4____ A

e.   7____ A

Last modified: Thursday, 25 September 2025, 10:03 AM