If A = {x ∈ R : x is rational} and B = {x ∈ R : x has a terminating or repeating decimal form}, what is correct?
Answer and explanation
Correct answer: A = B
A real number is rational exactly when it can be expressed as p/q with integers p and q, q ≠ 0. The decimal expansion of every rational number terminates or repeats periodically. Conversely, every terminating decimal can be converted to a fraction with a power of 10 as denominator, and every repeating decimal is also rational. Thus A and B contain exactly the same numbers, so A = B.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
A real number is rational exactly when it can be expressed as p/q with integers p and q, q ≠ 0. The decimal expansion of every rational number terminates or repeats periodically. Conversely, every terminating decimal can be converted to a fraction with a power of 10 as denominator, and every repeating decimal is also rational. Thus A and B contain exactly the same numbers, so A = B.
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.
