Question 5 of 35beginner🔧 ApplyShort Answer2 marks

If A={−1,1}A = \{-1, 1\}, find A×A×AA \times A \times A.

Correct Answer

A × A × A = {(-1,-1,-1), (-1,-1,1), (-1,1,-1), (-1,1,1), (1,-1,-1), (1,-1,1), (1,1,-1), (1,1,1)}

Exercise: EXERCISE 2.1 | Q: 5 | (Page 4)
For More Understanding

Explanation

This question tests the concept of Cartesian product of three sets. Following Example 4 from the textbook where P = {1, 2} and P × P × P is formed by taking all possible ordered triples, we apply the same method here. Since A has 2 elements, the Cartesian product A × A × A will have 2×22 \times 2 × 2 = 8 ordered triples. Each triple is formed by taking elements from A in all possible combinations.

Solution Steps

  1. Step 1: Given A = {-1, 1}, we need to find A × A × A which consists of all ordered triples (a, b, c) where a, b, c ∈ A.

  2. Step 2: Since A has 2 elements, the total number of elements in A × A × A = 2×22 \times 2 × 2 = 8.

  3. Step 3: Listing all possible ordered triples: {(-1,-1,-1), (-1,-1,1), (-1,1,-1), (-1,1,1), (1,-1,-1), (1,-1,1), (1,1,-1), (1,1,1)}

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