Question 2 of 33beginner🔧 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

The number of elements in (A×B)(A \times B) is 9.

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

Explanation

According to the textbook context, if there are pp elements in A and qq elements in B, then there will be pqpq elements in A×BA \times B. This is stated as: if n(A)=pn(A) = p and n(B)=qn(B) = q, then n(A×B)=pqn(A \times B) = pq. Since set A has 3 elements and set B = {3, 4, 5} also has 3 elements, the number of elements in (A×B)(A \times B) equals 3×33 \times 3 = 9.

Solution Steps

  1. Step 1: Given n(A) = 3 (set A has 3 elements)

  2. Step 2: Set B = {3, 4, 5}, so n(B) = 3

  3. Step 3: Using the formula n(A × B) = n(A) × n(B)

  4. Step 4: n(A × B) = 3×33 \times 3 = 9

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