Relations and Functions - I — Flashcards
NIOS · Class 12 · Mathematics
25 flashcards for Relations and Functions - I (NIOS Class 12 Mathematics) to test yourself on key terms and facts.
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If A = {1, 2, 3} and B = {a, b}, find n(A × B) and verify using the formula.
Answer
Formula: n(A × B) = n(A) × n(B) Step 1: Identify n(A) = 3 elements Step 2: Identify n(B) = 2 elements Step 3: Apply formula: n(A × B) = 3 × 2 = 6 Verification by listing: A × B = {(1,a), (1,b), (2,a…
Let A = {2, 3, 4} and B = {5, 6}. Find A × B and B × A. Is A × B = B × A?
Answer
Step 1: Find A × B (first element from A, second from B) A × B = {(2,5), (2,6), (3,5), (3,6), (4,5), (4,6)} Step 2: Find B × A (first element from B, second from A) B × A = {(5,2), (5,3), (5,4), (6,2…
Given A = {1, 3, 5}, B = {2, 4, 6}, C = {1, 4}. Find A × (B ∪ C).
Answer
Step 1: Find B ∪ C (union of B and C) B = {2, 4, 6}, C = {1, 4} B ∪ C = {1, 2, 4, 6} (combine all elements, count 4 only once) Step 2: Find A × (B ∪ C) A × (B ∪ C) = {(1,1), (1,2), (1,4), (1,6), (3,1…
Given A = {4, 5, 6, 7} and B = {8, 9}. Verify that A × (B - C) = (A × B) - (A × C) where C = {10}.
Answer
Step 1: Find B - C B = {8, 9}, C = {10} B - C = {8, 9} (no element of C is in B) Step 2: Find A × (B - C) A × (B - C) = {(4,8), (4,9), (5,8), (5,9), (6,8), (6,9), (7,8), (7,9)} Step 3: Find A × B an…
Define relation R from A = {2, 4, 6, 8} to B = {2, 3, 4, 5} by R = {(a,b): a ∈ A, b ∈ B and a is divisible by b}. Find R in roster form, domain, and range.
Answer
Step 1: Check each pair (a,b) where a is divisible by b - (2,2): 2÷2=1 ✓ - (2,3): 2÷3 ✗ - (2,4): 2÷4 ✗ - (2,5): 2÷5 ✗ - (4,2): 4÷2=2 ✓ - (4,3): 4÷3 ✗ - (4,4): 4÷4=1 ✓ - (4,5): 4÷5 ✗ - (6,2): 6÷2=3 ✓ -…
Given R = {(x,y): 4x + y = 12, x,y ∈ ℕ}, find R in roster form, domain, and range.
Answer
Step 1: Rearrange equation 4x + y = 12 y = 12 - 4x Step 2: Find valid pairs (x,y) where x,y ∈ ℕ (natural numbers: 1,2,3,...) - If x = 1: y = 12 - 4(1) = 8 ✓ - If x = 2: y = 12 - 4(2) = 4 ✓ - If x = 3…
Which of these relations is a function? Explain why or why not. (a) {(1,-2), (3,7), (4,-6), (8,1)}, A={1,3,4,8}, B={-2,7,-6,1,2} (b) {(1,0), (1,-1), (2,3), (4,10)}, A={1,2,4}, B={0,-1,3,10}
Answer
For a relation to be a function: ✓ Every element in domain must have exactly ONE image ✗ No element can map to multiple elements (a) {(1,-2), (3,7), (4,-6), (8,1)} Check: 1→-2, 3→7, 4→-6, 8→1 Each el…
Which of these relations from ℝ to ℝ represent functions? (a) y = 3x + 2 (b) y < x + 3 (c) y² = x
Answer
Rule: For each x ∈ domain, there must be exactly ONE y value (a) y = 3x + 2 For any real value x, there is exactly ONE corresponding y value Example: x=1 → y=3(1)+2=5 (only one answer) This IS a func…
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