Relations and Functions — Flashcards
ICSE · Class 12 · Mathematics
28 flashcards for Relations and Functions (ICSE Class 12 Mathematics) to test yourself on key terms and facts.
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Find the Cartesian product: A = {a, b, c} and B = {1, 2}.
Answer
Step 1: Write all ordered pairs with first element from A and second element from B. Step 2: Pair a with 1, 2; b with 1, 2; c with 1, 2. Step 3: A × B = {(a,1), (a,2), (b,1), (b,2), (c,1), (c,2)}. Ans…
How many elements are in A × B if n(A) = 3 and n(B) = 4?
Answer
Step 1: Use the formula n(A × B) = pq, where p = n(A) and q = n(B). Step 2: Substitute p = 3 and q = 4. Step 3: n(A × B) = 3 × 4 = 12. Answer: 12 elements.
If A or B is empty, what is A × B?
Answer
Step 1: The Cartesian product contains ordered pairs (a,b) with a in A and b in B. Step 2: If one set has no element, no ordered pair can be formed. Step 3: So A × B = ∅. Answer: The Cartesian product…
Write the number of relations from A to B when n(A) = p and n(B) = q, and find it for p = 3, q = 3.
Answer
Step 1: Any relation from A to B is a subset of A × B. Step 2: Number of elements in A × B = pq. Step 3: Number of subsets of A × B = 2^(pq). Step 4: For p = 3, q = 3, number of relations = 2^(3×3) = …
Let A = {1, 2, 3} and B = {2, 3, 4}. Find the relation R defined by 2a = b.
Answer
Step 1: Check each a in A. Step 2: For a = 1, b = 2 is in B, so (1,2) belongs to R. Step 3: For a = 2, b = 4 is in B, so (2,4) belongs to R. Step 4: For a = 3, b = 6 is not in B, so no pair. Answer: R…
What is the domain, co-domain, and range of R = {(2,6), (3,9)} from A = {2,3} to B = {6,9,12}?
Answer
Step 1: Domain is the set of first components. Step 2: Domain = {2,3}. Step 3: Co-domain is the target set B = {6,9,12}. Step 4: Range is the set of second components. Step 5: Range = {6,9}. Answer: D…
Find the inverse of R = {(2,3), (2,7), (3,7), (4,7)}.
Answer
Step 1: Reverse each ordered pair. Step 2: (2,3) becomes (3,2). Step 3: (2,7) becomes (7,2). Step 4: (3,7) becomes (7,3). Step 5: (4,7) becomes (7,4). Answer: R^(-1) = {(3,2), (7,2), (7,3), (7,4)}.
State the relation between domain and range of an inverse relation using R and R^(-1).
Answer
Step 1: Reverse ordered pairs when taking inverse. Step 2: First components of R become second components of R^(-1). Step 3: So Domain of R = Range of R^(-1). Step 4: Also, Range of R = Domain of R^(-…
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