Relations and Functions
Punjab Board · Class 11 · Mathematics
Flashcards for Relations and Functions — Punjab Board Class 11 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Find the values of x and y if (x + 1, y - 2) = (3, 1)
Answer
Since ordered pairs are equal, corresponding elements must be equal. Step 1: Equate first elements: x + 1 = 3 Step 2: Solve for x: x = 3 - 1 = 2 Step 3: Equate second elements: y - 2 = 1 Step 4: Solve…
If set A = {1, 2, 3} and set B = {4, 5}, find A × B and determine n(A × B)
Answer
Step 1: List all ordered pairs with first element from A and second from B A × B = {(1,4), (1,5), (2,4), (2,5), (3,4), (3,5)} Step 2: Count the elements n(A) = 3 (elements in A) n(B) = 2 (elements in …
Determine if A × B = B × A. If not, explain why with an example.
Answer
In general, A × B ≠ B × A (they are not equal). Example: Let A = {a, b} and B = {1, 2} A × B = {(a,1), (a,2), (b,1), (b,2)} B × A = {(1,a), (1,b), (2,a), (2,b)} These are different sets because: - In …
If P = {a, b} and Q = {3, 4, 5}, find (P × Q) ∩ (P × Q). What does this represent?
Answer
Step 1: Find P × Q P × Q = {(a,3), (a,4), (a,5), (b,3), (b,4), (b,5)} Step 2: Find (P × Q) ∩ (P × Q) Any set intersected with itself equals itself: (P × Q) ∩ (P × Q) = P × Q = {(a,3), (a,4), (a,5), (b…
For A = {1, 2, 3}, B = {2, 3, 4}, C = {3, 4, 5}, find A × (B ∩ C) and verify it equals (A × B) ∩ (A × C)
Answer
Step 1: Find B ∩ C B = {2, 3, 4}, C = {3, 4, 5} B ∩ C = {3, 4} Step 2: Find A × (B ∩ C) A × (B ∩ C) = {1, 2, 3} × {3, 4} = {(1,3), (1,4), (2,3), (2,4), (3,3), (3,4)} Step 3: Find (A × B) and (A × C) A…
Define the relation R = {(x, y) : y = 2x, x ∈ {1, 2, 3, 4}} in roster form. Find its domain and range.
Answer
Step 1: Generate ordered pairs using y = 2x When x = 1: y = 2(1) = 2 → (1, 2) When x = 2: y = 2(2) = 4 → (2, 4) When x = 3: y = 2(3) = 6 → (3, 6) When x = 4: y = 2(4) = 8 → (4, 8) Step 2: Write in ros…
Let A = {1, 2, 3, 4, 5, 6}. Define relation R = {(x, y) : y = x + 1} from A to A. Find domain, codomain, and range. Is this a function?
Answer
Step 1: Generate ordered pairs (y = x + 1) (1, 2), (2, 3), (3, 4), (4, 5), (5, 6) Note: (6, 7) cannot be included because 7 ∉ A Step 2: Identify domain, codomain, and range Domain = {1, 2, 3, 4, 5} (e…
Which of these relations is a function? Give reasons. (i) R₁ = {(2,1), (3,1), (4,2)} (ii) R₂ = {(2,2), (2,4), (3,3), (4,4)} (iii) R₃ = {(1,2), (2,3), (3,4), (4,5)}
Answer
Analyzing each relation: (i) R₁ = {(2,1), (3,1), (4,2)} - First elements: 2, 3, 4 (each appears once) - Each first element has exactly ONE second element ✓ IS A FUNCTION (ii) R₂ = {(2,2), (2,4), (3,3)…
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