Question 17 of 33intermediate🔧 ApplyVery Short1 mark

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

64

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

Explanation

This question tests the fundamental formula for counting relations between two sets. According to the textbook Note provided: 'If n(A) = p and n(B) = q, then n(A × B) = pq and the total number of relations is 2^(pq).' The key insight is that a relation from A to B is defined as a subset of A × B, so counting relations equals counting all possible subsets of the Cartesian product.

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

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

PreviousNext