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Subjects

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

In a Venn diagram, what set is B ∩ Aᶜ equal to?In a class, 58 students learn music, 49 learn painting, and 22 learn both. How many students learn at least one of the two arts?If n(A union B) = 97, n(A) = 63, and n(B − A) = 34, which conclusion about n(A intersection B) is correct?If A and B are disjoint sets, which of the following statements is correct?If n(A − B) = 32 and n(A intersection B) = 18, what is n(A)?If n(A union B) = 92, n(A − B) = 35, and n(A intersection B) = 24, what is n(B − A)?In a Venn diagram, n(A ∩ B) = 0 and n(A ∪ B) = 76. If n(A) = 31, what is n(B)?If n(A) = 68, n(B) = 53, and n(A ∪ B) = 91, what is n(A ∩ B)?If n(B) = 66 and n(A ∩ B) = 31, how many elements are only in B, that is, in B but not in A?If n(A−B)=38 and n(B−A)=27, what is n(A△B), the cardinality of the symmetric difference?Let U={1,2,3,4,5,6,7,8,9,10,11,12}, A={2,4,6,8,10,12}, and B={3,4,6,9,12}. What is A∩B?If A={a,c,e,g,i} and B={b,c,d,g,j}, what is A∪B?A={5,10,15,20,25,30} and B={10,20,30,40}. What is A−B?For two sets A and B, n(A)=54, n(B)=61, and 73 elements belong to exactly one of the sets. What is n(A∩B)?In a class, 63 students learn dance, 58 learn music, and 26 learn both. How many students learn at least one art?In a group, 52 people like apples, 47 like bananas, and 19 like both. How many people like only apples?If n(A − B) = 41 and n(A ∩ B) = 22, what is n(A)?If n(A ∪ B) = 104, n(A − B) = 46, and n(A ∩ B) = 25, what is n(B − A)?If n(U) = 125, n(A) = 62, n(B) = 55, and n((A ∪ B)ᶜ) = 24, what is n(A ∩ B)?In a Venn diagram, n(A ∩ B) = 0 and n(A ∪ B) = 92. If n(A) = 40, what is n(B)?