Are the following pair of sets equal? Give reasons.
(i) A = {2, 3}; B = {x: x is solution of \(x^2+ 5x + 6 = 0\)}
(ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}
(i) A = {2, 3}; B = {x: x is solution of \(x^2+ 5x + 6 = 0\)}
(ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}
Solution and Explanation
(i) A = {2, 3}; B = {x: x is a solution of \(x^2+ 5x + 6 = 0\)}
The equation \(x^2+ 5x + 6 = 0\) can be solved as:
\(x(x + 3) + 2(x + 3) = 0 (x + 2)(x + 3) = 0\)
\(x = -2 \) or \(x = -3\)
∴ A = {2, 3}; B = {-2, -3}
∴ \(A ≠ B\)
(ii) A = {x: x is a letter in the word FOLLOW} = {F, O, L, W}
B = {y: y is a letter in the word WOLF} = {W, O, L, F}
The order in which the elements of a set are listed is not significant.
A = B
Top Questions on Equal Sets
- Let A= {1, 2, {3, 4,}, 5}. Which of the following statements are incorrect and why?
(i) {3, 4} \(⊂\) A
(ii) {3, 4}}\(∈\) A
(iii) {{3, 4}}\(⊂\) A
(iv) 1\(∈\) A
(v) 1\(⊂\) A
(vi) {1, 2, 5} \(⊂\) A
(vii) {1, 2, 5}\(∈\) A
(viii) {1, 2, 3} \(⊂\) A
(ix) \( \phi ∈A\)
(x) \( \phi⊂ A\)
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Concepts Used:
Operations on Sets
Some important operations on sets include union, intersection, difference, and the complement of a set, a brief explanation of operations on sets is as follows:
1. Union of Sets:
- The union of sets lists the elements in set A and set B or the elements in both set A and set B.
- For example, {3,4} ∪ {1, 4} = {1, 3, 4}
- It is denoted as “A U B”
2. Intersection of Sets:
- Intersection of sets lists the common elements in set A and B.
- For example, {3,4} ∪ {1, 4} = {4}
- It is denoted as “A ∩ B”
3.Set Difference:
- Set difference is the list of elements in set A which is not present in set B
- For example, {3,4} - {1, 4} = {3}
- It is denoted as “A - B”
4.Set Complement:
- The set complement is the list of all elements present in the Universal set except the elements present in set A
- It is denoted as “U-A”