Relations and Functions — Flashcards
Punjab Board · Class 11 · Mathematics
25 flashcards for Relations and Functions (Punjab Board Class 11 Mathematics) to test yourself on key terms and facts.
Interactive on Super Tutor
Studying Relations and Functions? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for flashcards and more.
Free trial, no card needed.
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)…
+17 more flashcards
Practise AllFrequently Asked Questions
What are the important topics in Relations and Functions for Punjab Board Class 11 Mathematics?
How many flashcards are available for Relations and Functions?
How should I revise Relations and Functions for Class 11 exams?
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Relations and Functions
For serious students
Get the full Relations and Functions chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Punjab Board Class 11 Mathematics. Free to start, no card needed.