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 33intermediate🔍 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 understanding of Cartesian products. From the definition, if (a, b) ∈ A × B, then a ∈ A and b ∈ B. The first elements of all ordered pairs in A × B must belong to set A, and the second elements must belong to set B. Since n(A) = 3 and the first elements x, y, z are distinct, these must be exactly the three elements of A. Similarly, since n(B) = 2 and the second elements appearing are 1 and 2, these must be the two elements of B.

Solution Steps

Step 1: From the definition of Cartesian product, if (a, b) ∈ A × B, then a ∈ A and b ∈ B.
Step 2: From the given ordered pairs (x, 1), (y, 2), (z, 1), the first elements are x, y, z and the second elements are 1, 2.
Step 3: Since x, y, z are distinct elements and n(A) = 3, therefore A = {x, y, z}.
Step 4: Since the second elements are 1 and 2, and n(B) = 2, therefore B = {1, 2}.

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