Question 6 of 35beginner🔧 ApplyShort Answer2 marks

If A×B={(a,x),(a,y),(b,x),(b,y)}A \times B = \{(a, x), (a, y), (b, x), (b, y)\}. Find AA and BB.

Correct Answer

A = {a, b} and B = {x, y}

Exercise: EXERCISE 2.1 | Q: 6 | (Page 4)
For More Understanding

Explanation

This question tests the understanding of Cartesian products. The Cartesian product A × B consists of all ordered pairs (x, y) where x ∈ A and y ∈ B. To find the original sets A and B from their Cartesian product, we extract the first elements to form set A and the second elements to form set B. This is demonstrated in Example 6 of the textbook context.

Solution Steps

  1. Step 1: Identify all first elements from the ordered pairs in A × B = {(a, x), (a, y), (b, x), (b, y)}. The first elements are: a, a, b, b.

  2. Step 2: The set A is formed by taking unique first elements. Therefore, A = {a, b}.

  3. Step 3: Identify all second elements from the ordered pairs. The second elements are: x, y, x, y.

  4. Step 4: The set B is formed by taking unique second elements. Therefore, B = {x, y}.

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