If X = {x : x ∈ N, x² is odd and x < 8}, what is X?
Answer and explanation
Correct answer: X = {1, 3, 5, 7}
The square of an integer is odd if and only if the integer itself is odd. The natural numbers less than 8 are 1 through 7, and the odd members among them are 1, 3, 5, and 7. Therefore X = {1, 3, 5, 7}. The value 0 is not included under the positive-natural-number convention, and even numbers have even squares. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
X = {1, 3, 5, 7}
Why is this the correct answer?
The square of an integer is odd if and only if the integer itself is odd. The natural numbers less than 8 are 1 through 7, and the odd members among them are 1, 3, 5, and 7. Therefore X = {1, 3, 5, 7}. The value 0 is not included under the positive-natural-number convention, and even numbers have even squares. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
