Which of the following sets are equal? A = {1, 2, 3}, B = {x ∈ R : x² – 2x + 1 = 0}, C = {1, 2, 2, 3}, D = {x ∈ R : x³ – 6x²+11x – 6 = 0}.

Solution:

Sets are very important concepts that are used to analyze data and the relationship between data items. Using the concepts of Venn diagrams, we can represent two or more categories and show the common items among them. We can also check for equality of given sets, and solve many similar problems using this concept.

Let's understand the solution to this question.

⇒ For set B; we have the equation x² – 2x + 1 = 0, whose solutions are x = 1, 1. Hence set B can be written as {1, 1}.

⇒ For set D; we have the equation x³ – 6x²+11x – 6 = 0, whose solutions are x = 1, 2, 3. Hence set D can be written as {1, 2, 3}.

⇒ The sets A and C are equal since they have the same number of distinct items, that is, 1, 2, and 3.

⇒ Similarly, set D is also equal to sets A and C.

Hence, among the given sets, A, C and D are equal.

Which of the following sets are equal? A = {1, 2, 3}, B = {x ∈ R : x² – 2x + 1 = 0}, C = {1, 2, 2, 3}, D = {x ∈ R : x³ – 6x²+11x – 6 = 0}.

Summary:

Among the given sets, A, C and D are equal.