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 = {x ∈ N : x ≤ 40 and x is a perfect square} and B = {x ∈ N : x ≤ 40 and x is even}, where N denotes the positive natural numbers, what is A ∩ B?If A ∩ B = B ∩ C = C ∩ A = ∅, |A| = 9, |B| = 11, and |C| = 13, what is |A ∪ B ∪ C|?If A \ (B ∩ C) = ∅, which statement must be true?If A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8}, and C = {1, 4, 6, 9}, what is A \ (B ∩ C)?Using (A \ B) ∪ (A ∩ B) = A, how are these two parts of A related?If A ∪ B = B ∪ C and A ∩ B = B ∩ C, which conclusion must be true?If A and B are finite sets, |A ∪ B| = 65, |A ∩ B| = 18, and |A| = 39, what is |B \ A|?If A = {x ∈ R | x² − 9 = 0} and B = {x ∈ R | x² − 6x + 9 = 0}, what is A ∪ B?If A ⊆ B, what is (C \ B) ∩ A?In which situation can A \ B = A ∩ B be true?If A ∩ B ⊆ A \ C, which statement must be true?If A ∪ B = A ∩ C, which conclusion must be true?Let U = {1, 2, ..., 50}, A = {x ∈ U | 2 divides x}, and B = {x ∈ U | 5 divides x}. How many elements are in A \ B?If A ∩ B = ∅ and A ∪ B = A ∪ C, which conclusion must be true?If A = {a,b,c,d,e}, B = {b,d,f,g}, and C = {a,d,g,h}, what is (A ∩ C) ∪ (B \ A)?If |A| = 30, |B| = 27, |C| = 25, |A ∩ B| = 12, |B ∩ C| = 10, |C ∩ A| = 8, and |A ∩ B ∩ C| = 4, what is |A ∪ B ∪ C|?If A \ B = C \ B and A ∩ B = C ∩ B, what conclusion follows?If A \ (B \ C) = A, which inclusion must be true?If A ∩ B = A ∩ C and A \ B = A \ C, which conclusion must be true?In a survey of 150 people, 88 are in tea set T, 76 are in coffee set C, and 39 are in both. How many drink only tea?