If A = {x ∈ ℤ : x² = 25}, B = {5, −5}, and C = {−5, 5, 5}, which statement is correct?
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Answer and explanation
Correct answer: A = B = C
Solving x² = 25 gives x = 5 or x = −5, so A = {5, −5}. This is exactly the same collection of elements as B. In set notation, repeated listing of an element does not create a new element; therefore C = {−5, 5, 5} is simply {−5, 5}. Consequently, all three sets have the same elements and A = B = C.
Frequently asked questions
What is the correct answer to this question?
A = B = C
Why is this the correct answer?
Solving x² = 25 gives x = 5 or x = −5, so A = {5, −5}. This is exactly the same collection of elements as B. In set notation, repeated listing of an element does not create a new element; therefore C = {−5, 5, 5} is simply {−5, 5}. Consequently, all three sets have the same elements and A = B = C.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
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