Mathematics
Operations on Sets (Union, Intersection, Difference)
समुच्चयों पर संक्रियाएँ (संघ, प्रतिच्छेद और अंतर)
In Class 11 Mathematics, the Sets chapter introduces Operations on Sets (Union, Intersection, Difference). Students learn to combine sets using union, identify common elements through intersection, and find elements belonging to one set but not another using difference. They also apply these operations to subset relations, Venn diagrams, and problems involving the number of elements in sets.
Practice questions
If A ∪ B = A and B ∪ C = C, which relation must be true?If A = {x ∈ N : x ≤ 25 and x is odd} and B = {x ∈ N : x ≤ 25 and 3 divides x}, what is |A ∩ B|?If A \ C = B \ C, which statement is always true?If \(A\setminus B\subseteq A\cap C\), which conclusion must be true?If \(A=\{1,3,5,7,9,11\}\), \(B=\{3,6,9,12\}\), and \(C=\{5,9,13\}\), what is the value of \((A\setminus B)\cap C\)?If \(A\cup(B\cap C)=A\), which inclusion must be true?If \(A=[1,10]\), \(B=[3,7]\), and \(C=(5,12)\), what is \(A\setminus(B\cup C)\)?If \(|A\cup B|=92\), \(|A\setminus B|=31\), and \(|A\cap B|=27\), what is \(|B|\)?If \(A\setminus B=A\setminus C\) and \(B\subseteq C\), which conclusion must be true?If \(A\), \(B\), and \(C\) are finite sets and \(A\cap B\cap C=\varnothing\), which formula for \(|A\cup B\cup C|\) is correct?If \(A\setminus B\ne\varnothing\) and \(B\setminus A=\varnothing\), which statement is correct?If A ∩ (B \ C) = A ∩ B, which conclusion must be true?If A = {x : x ∈ N, x ≤ 60, 4 divides x} and B = {x : x ∈ N, x ≤ 60, 6 divides x}, what is |A \ B|?If A ∪ B = A △ B, where A △ B = (A \ B) ∪ (B \ A), which conclusion must be true?If A = [−3, 4], B = (−1, 6), and C = [2, 8], what is A ∩ (B \ C)?If the universal set is \(U=\{2,4,6,8,10,12\}\) and \(A=\{4,8,12\}\), what is the value of \(U-A\)?If \(|U|=150\), \(|A'|=92\), \(|B'|=76\), and \(|A\cap B|=31\), what is \(|(A\cup B)'|\)?In a group of 150 students, 82 study mathematics, 74 study biology, and 36 study both subjects. How many study neither subject?