Relations and Functions
ICSE · Class 11 · Mathematics
Flashcards for Relations and Functions — ICSE Class 11 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Explore the full setFind A × B when A = {1, 2} and B = {a, b}.
Answer
Step 1: Use the Cartesian product rule: A × B = {(x, y): x ∈ A and y ∈ B}. Step 2: Pair each element of A with each element of B. A × B = {(1, a), (1, b), (2, a), (2, b)}. Answer: {(1, a), (1, b), (2,…
Find B × A when A = {1, 2} and B = {a, b}.
Answer
Step 1: Switch the order of the sets. Step 2: Form ordered pairs with first element from B and second element from A. B × A = {(a, 1), (a, 2), (b, 1), (b, 2)}. Step 3: Compare with A × B. A × B ≠ B × …
If n(A) = 3 and n(B) = 4, find n(A × B).
Answer
Step 1: Use the formula n(A × B) = pq. Here, p = 3 and q = 4. Step 2: Multiply. n(A × B) = 3 × 4 = 12. Answer: 12…
If A = {a, b, c} and B = {x, y}, how many ordered pairs are in A × B?
Answer
Step 1: Count elements in each set. n(A) = 3, n(B) = 2. Step 2: Use n(A × B) = pq. n(A × B) = 3 × 2 = 6. Step 3: The pairs are (a, x), (a, y), (b, x), (b, y), (c, x), (c, y). Answer: 6 ordered pairs…
Find A × (B ∩ C) when A = {1, 2, 3}, B = {3, 4}, and C = {4, 5, 6}.
Answer
Step 1: Find the intersection. B ∩ C = {4}. Step 2: Form the Cartesian product with A. A × (B ∩ C) = A × {4}. Step 3: Write all ordered pairs. A × (B ∩ C) = {(1, 4), (2, 4), (3, 4)}. Answer: {(1, 4), …
Show that A × (B ∪ C) = (A × B) ∪ (A × C) using A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}.
Answer
Step 1: Find the union. B ∪ C = {3, 4, 5, 6}. Step 2: Form A × (B ∪ C). A × (B ∪ C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}. Step 3: Form A ×…
Is R = {(1, a), (2, c)} a function from A = {1, 2, 3} to B = {a, b, c}?
Answer
Step 1: Check whether every element of A has exactly one image. Step 2: Element 1 has one image and element 2 has one image. Step 3: Element 3 has no image. A function must give each element of A exac…
Is R = {(1, a), (1, b), (3, c)} a function from A = {1, 2, 3} to B = {a, b, c}?
Answer
Step 1: Check the images of each element of A. Step 2: Element 1 has two images: a and b. Step 3: A function cannot give more than one image to the same element. Answer: No, it is not a function.
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