ICSE Class 12 Mathematics — Flashcards for Quick Revision

A: 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

A: 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.

A: 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

A: Step 1: Check each element of A. 1 maps to a. 2 maps to c. 3 maps to b. Step 2: Every element of the domain has exactly one image. Answer: R is a function.

A: Step 1: Look at element 1. It has two images: a and b. Step 2: A function cannot give two images to the same domain element. Answer: R is not a function.

A: Step 1: Domain is the set of first elements. Domain = {1, 2, 3} Step 2: Co-domain is the given target set. Co-domain = {5, 6, 7, 8} Step 3: Range is the set of actual images. Range = {5, 6, 7} Answer:

A: Step 1: Substitute a = 2 and b = 3. Step 2: Compute 2 * 3 = 2 + 3. Step 3: 2 + 3 = 5. Answer: 5 Check: The result is a real number, so the operation is closed on R.

A: Step 1: Test closure on N. Step 2: Take a = 1 and b = 2. Step 3: 1 - 2 = -1. Step 4: -1 is not in N. Answer: No, it is not a binary operation on N.

A: Step 1: Use the formula Number of binary operations on A = p^(p^2). Step 2: Here p = 3. Step 3: So the number is 3^(3^2) = 3^9. Answer: 3^9 Meaning: A binary operation is a function from A × A to A, s