Question 2 of 35beginner🔧 ApplyVery Short1 mark

If the set AA has 3 elements and the set B={3,4,5}B = \{3, 4, 5\}, then find the number of elements in (A×B)(A \times B).

Correct Answer

9

Exercise: EXERCISE 2.1 | Q: 2 | (Page 4)
For More Understanding

Explanation

This is a direct application of the cartesian product property stated in the textbook context: 'If there are p elements in A and q elements in B, then there will be pq elements in A × B, i.e., if n(A) = p and n(B) = q, then n(A × B) = pq.' The set A has 3 elements (given), and set B = {3, 4, 5} also has 3 elements. Therefore, n(A × B) = 3×33 \times 3 = 9.

Solution Steps

  1. Step 1: Given n(A) = 3 and B = {3, 4, 5}, so n(B) = 3

  2. Step 2: Using the formula n(A × B) = n(A) × n(B)

  3. Step 3: n(A × B) = 3×33 \times 3 = 9

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