Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1),…

Question 9 of 35intermediate🔍 AnalyzeShort Answer2 marks

Let $A$ and $B$ be two sets such that $n(A) = 3$ and $n(B) = 2$ . If $(x, 1), (y, 2), (z, 1)$ are in $A \times B$ , find $A$ and $B$ , where $x, y$ and $z$ are distinct elements.

Correct Answer

A = {x, y, z} and B = {1, 2}

Exercise: EXERCISE 2.1 | Q: 9 | (Page 4)

For More Understanding

Explanation

This question tests the understanding of Cartesian products. From Example 6 in the textbook, we learn that for any Cartesian product A × B, set A consists of all first elements of the ordered pairs, and set B consists of all second elements. Given the ordered pairs (x, 1), (y, 2), (z, 1) in A × B, we extract the first elements {x, y, z} to form set A, and the second elements {1, 2} to form set B. The conditions n(A) = 3 and n(B) = 2 are satisfied since A has exactly 3 distinct elements (x, y, z are distinct) and B has exactly 2 distinct elements (1 and 2).

Solution Steps

Step 1: From the ordered pairs (x, 1), (y, 2), (z, 1) in A × B, identify the first elements: x, y, z
Step 2: Identify the second elements: 1, 2, 1
Step 3: Set A = set of first elements = {x, y, z} (since x, y, z are distinct, n(A) = 3 ✓)
Step 4: Set B = set of second elements = {1, 2} (n(B) = 2 ✓)

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