Relations and Functions — Flashcards
Tamil Nadu Board · Class 10 · Mathematics
24 flashcards for Relations and Functions (Tamil Nadu Board Class 10 Mathematics) to test yourself on key terms and facts.
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Find A × B where A = {1, 2, 3} and B = {a, b}. How many elements will A × B have?
Answer
Step 1: A × B contains all ordered pairs (x, y) where x ∈ A and y ∈ B. Step 2: For each element in A, pair it with each element in B: - 1 pairs with: a, b → (1,a), (1,b) - 2 pairs with: a, b → (2,a), …
If n(A × B) = 20 and n(A) = 4, find n(B).
Answer
Step 1: Use the formula: n(A × B) = n(A) × n(B) Step 2: Substitute the given values: 20 = 4 × n(B) Step 3: Divide both sides by 4: n(B) = 20 ÷ 4 = 5 Answer: n(B) = 5 Explanation: The total number of o…
When should you use A × B instead of B × A? Explain with an example.
Answer
Use A × B when you need the Cartesian product with first coordinates from A and second coordinates from B. Example: If A = {Roll Numbers} and B = {Names}, then: - A × B = {(1, Raj), (2, Priya), ...} -…
Identify which of these sets are relations from A = {1,2,3} to B = {p,q}: (i) {(1,p), (2,q), (3,p)} (ii) {(1,p), (2,p), (2,q)} (iii) {(1,p), (q,2), (3,q)}
Answer
A relation from A to B must be a subset of A × B. First, find A × B = {(1,p), (1,q), (2,p), (2,q), (3,p), (3,q)} (i) {(1,p), (2,q), (3,p)} ✓ RELATION All ordered pairs have first coordinate from A an…
Find the domain, co-domain, and range of the relation R = {(2,4), (3,6), (5,10)} from A = {1,2,3,4,5} to B = {2,4,6,8,10,12}.
Answer
Step 1: Identify domain (first coordinates that appear in R): Domain = {2, 3, 5} ⊂ A Step 2: Identify co-domain (the set B given in the relation definition): Co-domain = B = {2,4,6,8,10,12} Step 3: …
Write the relation R = {(x,y) | y = x + 2, x ∈ {1,2,3,4}} in roster form. Is it a function?
Answer
Step 1: Find all ordered pairs by substituting values of x: When x = 1: y = 1 + 2 = 3 → (1,3) When x = 2: y = 2 + 2 = 4 → (2,4) When x = 3: y = 3 + 2 = 5 → (3,5) When x = 4: y = 4 + 2 = 6 → (4,6) Ste…
Determine whether f = {(1,2), (2,3), (1,4), (3,5)} is a function. Explain why or why not.
Answer
Step 1: Check if every element in domain has exactly one image. Step 2: Examine the pairs: - Element 1 appears twice: (1,2) and (1,4) - This means 1 has TWO different images: 2 and 4 Step 3: Apply f…
Evaluate f(3) and f(-1) where f(x) = x² - 2x + 5.
Answer
For f(x) = x² - 2x + 5: Step 1: Find f(3) Substitute x = 3: f(3) = (3)² - 2(3) + 5 f(3) = 9 - 6 + 5 f(3) = 8 Step 2: Find f(-1) Substitute x = -1: f(-1) = (-1)² - 2(-1) + 5 f(-1) = 1 + 2 + 5 f(-1) =…
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