Sets
Uttar Pradesh Board · Class 11 · Mathematics
Flashcards for Sets — Uttar Pradesh Board Class 11 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
If A = {2, 4, 6, 8} and B = {1, 2, 3, 4}, find A ∪ B
Answer
Step 1: List all elements from both sets A = {2, 4, 6, 8} B = {1, 2, 3, 4} Step 2: Combine all elements, taking common elements only once A ∪ B = {1, 2, 3, 4, 6, 8} Answer: A ∪ B = {1, 2, 3, 4, 6, 8
Find A ∩ B if A = {x : x is a prime number < 10} and B = {x : x is an odd number < 10}
Answer
Step 1: Write A in roster form Prime numbers < 10: A = {2, 3, 5, 7} Step 2: Write B in roster form Odd numbers < 10: B = {1, 3, 5, 7, 9} Step 3: Find common elements A ∩ B = {3, 5, 7} Answer: A ∩ B
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 4, 6, 8}, find A'
Answer
Step 1: Identify the universal set U U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Step 2: Identify set A A = {2, 4, 6, 8} Step 3: Find A' (complement of A) A' = elements in U but not in A A' = {1, 3, 5, 7, 9
Express the set {x : x² - 5x + 6 = 0} in roster form
Answer
Step 1: Solve the equation x² - 5x + 6 = 0 Factoring: (x - 2)(x - 3) = 0 Step 2: Find the values of x x - 2 = 0 → x = 2 x - 3 = 0 → x = 3 Step 3: Write in roster form The set = {2, 3} Answer: {2, 3
If A = {1, 2, 3} and B = {3, 4, 5}, find A - B and B - A
Answer
Step 1: Find A - B (elements in A but not in B) A = {1, 2, 3}, B = {3, 4, 5} A - B = {1, 2} Step 2: Find B - A (elements in B but not in A) B - A = {4, 5} Step 3: Verify Common element: 3 A - B remo
In a class of 30 students, 18 like Mathematics, 12 like Physics, and 6 like both. How many like neither subject?
Answer
Step 1: Use Venn diagram approach Let M = students liking Math, P = students liking Physics |M| = 18, |P| = 12, |M ∩ P| = 6 Step 2: Apply formula for union |M ∪ P| = |M| + |P| - |M ∩ P| |M ∪ P| = 18
Verify De Morgan's Law: (A ∪ B)' = A' ∩ B' using A = {1, 3, 5} and B = {2, 3, 4} with U = {1, 2, 3, 4, 5, 6}
Answer
Step 1: Find A ∪ B A ∪ B = {1, 2, 3, 4, 5} Step 2: Find (A ∪ B)' (A ∪ B)' = {6} Step 3: Find A' and B' A' = {2, 4, 6} B' = {1, 5, 6} Step 4: Find A' ∩ B' A' ∩ B' = {6} Step 5: Verify (A ∪ B)' = {6
Find the number of subsets of A = {a, b, c, d}
Answer
Step 1: Use the formula for number of subsets If a set has n elements, it has 2ⁿ subsets Step 2: Count elements in A n(A) = 4 elements Step 3: Calculate Number of subsets = 2⁴ = 16 Step 4: List to
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