Sets — Flashcards
NIOS · Class 12 · Mathematics
32 flashcards for Sets (NIOS Class 12 Mathematics) to test yourself on key terms and facts. Sample: "Problem: Given A = {1, 2, 3, 4, 5} and B ="
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Problem: Given A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}, find A ∩ B and explain what this operation means.
Answer
Step 1: Identify the intersection - find elements common to both sets Step 2: Check each element of A against B: 1(no), 2(no), 3(yes), 4(yes), 5(yes) Step 3: Write the result: A ∩ B = {3, 4, 5} Expla…
Problem: Given U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 4, 6, 8, 10}, find A' (complement of A).
Answer
Step 1: Identify the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Step 2: Identify set A = {2, 4, 6, 8, 10} Step 3: Find A' by listing all elements in U that are NOT in A Step 4: A' = {1, 3, 5, 7…
Problem: Find A ∪ B where A = {a, e, i, o, u} and B = {a, b, c, d, e}. What is the cardinality of A ∪ B?
Answer
Step 1: Identify union - collect all elements from both sets Step 2: List elements from A: a, e, i, o, u Step 3: Add elements from B that are NOT already listed: b, c, d Step 4: A ∪ B = {a, b, c, d, e…
Problem: Given A = {1, 2, 3, 4} and B = {2, 4, 6}, calculate A - B and B - A. Are they equal?
Answer
For A - B: Step 1: Find elements in A that are NOT in B Step 2: Check each: 1(yes, not in B), 2(no, in B), 3(yes, not in B), 4(no, in B) Step 3: A - B = {1, 3} For B - A: Step 1: Find elements in B t…
Problem: Write the set {x : x ∈ ℕ and 5 < x ≤ 10} in roster form and identify if it's finite or infinite.
Answer
Step 1: Understand the set-builder notation: natural numbers greater than 5 but less than or equal to 10 Step 2: List all natural numbers satisfying the condition: 6, 7, 8, 9, 10 Step 3: Roster form =…
Problem: Write the set of all even prime numbers in set-builder form and in roster form. Is it infinite?
Answer
Step 1: Identify even prime numbers (prime numbers divisible by 2) Step 2: The only even prime number is 2 (all other even numbers are divisible by 2 and not prime) Step 3: Roster form = {2} Step 4: S…
Problem: Given A = {1, 2, 3} and B = {1, 2, 3, 4, 5}, determine if A ⊆ B, A ⊂ B, or neither. Explain the difference.
Answer
Step 1: Check if every element of A is in B 1 ∈ B? YES 2 ∈ B? YES 3 ∈ B? YES Step 2: All elements of A are in B, so A ⊆ B (A is a subset of B) Step 3: Check if A ≠ B A has 3 elements, B has 5…
Problem: Set A has n(A) = 4. How many subsets does A have? How many PROPER subsets?
Answer
Step 1: Use the formula for number of subsets = 2^n, where n is the number of elements Step 2: Number of subsets = 2^4 = 16 Step 3: These 16 subsets include the empty set (∅) and the set A itself Ste…
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