Question 5 of 33beginner🔧 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 was formed, we apply the same method. The Cartesian product A × A × A consists of all ordered triples (a, b, c) where each component a, b, c belongs to set A. Since A has 2 elements, the total number of ordered triples is 2×22 \times 2 × 2 = 8.

Solution Steps

  1. Step 1: Identify that A × A × A requires forming ordered triples (a, b, c) where a ∈ A, b ∈ A, c ∈ A

  2. Step 2: Since A = {-1, 1}, each component can take values -1 or 1

  3. Step 3: List all 8 ordered triples systematically: (-1,-1,-1), (-1,-1,1), (-1,1,-1), (-1,1,1), (1,-1,-1), (1,-1,1), (1,1,-1), (1,1,1)

PreviousNext