If \(A=\{x\in\mathbb{N}:x\le 4\}\) and \(B=\{x\in\mathbb{N}:x<5\}\), which statement is correct?
Answer and explanation
Correct answer: \(A=B\)
For natural numbers, the condition \(x\le4\) selects \(1,2,3,4\) under the usual convention \(\mathbb N=\{1,2,3,\ldots\}\). The condition \(x<5\) selects exactly the same natural numbers, because a natural number less than 5 must be one of 1, 2, 3, or 4. Thus both sets have the same elements: \(A=B=\{1,2,3,4\}\). Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
For natural numbers, the condition \(x\le4\) selects \(1,2,3,4\) under the usual convention \(\mathbb N=\{1,2,3,\ldots\}\). The condition \(x<5\) selects exactly the same natural numbers, because a natural number less than 5 must be one of 1, 2, 3, or 4. Thus both sets have the same elements: \(A=B=\{1,2,3,4\}\). Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
