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Equal Sets

Let A be the set containing letters of the word in SITTING and B be the set containing letters of the word in STING, then A = {S, I, T, N, G} and B = {S, T, I, N, G}. We note that each element of A is an element of B and each element of B is an element of A. If such a thing happens, we say that the two sets A and B are equal and write A = B.

Definition:
Two sets A and B are said to be equal if they have exactly the same elements and we write A = B. Otherwise, the sets are said to be unequal and we write AB.

Illustration 1
Let A be the set of all integers satisfying the equation x2 = 4 and B = {2, -2}, then A = B.

Illustration 2
Let A = {1, 2, 3, 4} and , then A = B.

Illustration 3
Let A = {1, 2, 5, 7} and B = {1, 3, 5, 7}. Note that 2  B, therefore A is not equal to B. In this case, we write A B.

Illustration 4

In this problem none of the elements in the set C are in the set D. Therefore C is not equal to D

Illustration 5
Let A = {x : x is human being living on the earth and age 500 years} and B = {x : x is positive integer less than zero}, then A = B, because both A and B are empty sets.

Example
Which of the following sets are equal?
  1. A = {x : x is a letter of the word WOLF}
  2. B = {x : x is a letter of the word FOLLOW}
  3. C = {x : x is a letter of the word FLOWER}
  4. D = {x : x is a letter of the word FOLLOWER}
  5. E = {x : x is a letter of the word FLOW}
Solution
A = B = E and C = D




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