Question 17 of 35intermediate🔧 ApplyShort Answer2 marks

Let A={x,y,z}A = \{x, y, z\} and B={1,2}B = \{1, 2\}. Find the number of relations from AA to BB.

Correct Answer

The number of relations from A to B is 64.

Exercise: EXERCISE 2.2 | Q: 8 | (Page 7)
For More Understanding

Explanation

According to the textbook, the total number of relations from set A to set B equals the number of possible subsets of A × B. If n(A) = p and n(B) = q, then n(A × B) = pq, and the total number of relations is 2pq2^{pq}. Here, n(A) = 3 and n(B) = 2, so n(A × B) = 6, giving 262^{6} = 64 relations.

Solution Steps

  1. Step 1: Find n(A) and n(B). Given A = {x, y, z}, n(A) = 3. Given B = {1, 2}, n(B) = 2.

  2. Step 2: Calculate n(A × B) = n(A) × n(B) = 3×23 \times 2 = 6.

  3. Step 3: Apply the formula for number of relations. Number of relations = 2n2^{n}(A×B) = 262^{6} = 64.

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