If \(A=\{x:x=2k,\ k\in\mathbb{Z}\}\) and \(B=\{x:x=4k,\ k\in\mathbb{Z}\}\), which relation is correct?
Answer and explanation
Correct answer: \(B\subseteq A\)
Set \(A\) is the set of all even integers, while set \(B\) is the set of all integers divisible by 4. Every number of the form \(4k\) can be written as \(2(2k)\), so it is also an element of \(A\). However, 2 belongs to \(A\) but not to \(B\). Therefore, \(B\subseteq A\), but \(A\not\subseteq B\).
Frequently asked questions
What is the correct answer to this question?
\(B\subseteq A\)
Why is this the correct answer?
Set \(A\) is the set of all even integers, while set \(B\) is the set of all integers divisible by 4. Every number of the form \(4k\) can be written as \(2(2k)\), so it is also an element of \(A\). However, 2 belongs to \(A\) but not to \(B\). Therefore, \(B\subseteq A\), but \(A\not\subseteq B\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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