If \(A\subseteq B\), then what is \(A\cup B\) equal to?
Answer and explanation
Correct answer: \(B\)
The relation \(A\subseteq B\) means that every element of \(A\) is already contained in \(B\). The union collects all elements from both sets, but adding the elements of \(A\) contributes nothing new because they are already in \(B\). Consequently, \(A\cup B=B\). In contrast, \(A\cap B=A\) and \(A\setminus B=\varnothing\) under this condition.
Frequently asked questions
What is the correct answer to this question?
\(B\)
Why is this the correct answer?
The relation \(A\subseteq B\) means that every element of \(A\) is already contained in \(B\). The union collects all elements from both sets, but adding the elements of \(A\) contributes nothing new because they are already in \(B\). Consequently, \(A\cup B=B\). In contrast, \(A\cap B=A\) and \(A\setminus B=\varnothing\) under this condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
