Which statement is correct about the set A = {x ∈ Q : x² = 0.25}?
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Answer and explanation
Correct answer: A = {-0.5, 0.5}; it is finite
Since 0.25 = 1/4, the equation x² = 0.25 becomes x² = (1/2)². A square equation has both the positive and negative square roots, so x = 1/2 or x = -1/2. Both values are rational and must be included. Hence A = {-0.5, 0.5}, a finite set containing two elements.
Frequently asked questions
What is the correct answer to this question?
A = {-0.5, 0.5}; it is finite
Why is this the correct answer?
Since 0.25 = 1/4, the equation x² = 0.25 becomes x² = (1/2)². A square equation has both the positive and negative square roots, so x = 1/2 or x = -1/2. Both values are rational and must be included. Hence A = {-0.5, 0.5}, a finite set containing two elements.
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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