Question

The Cartesian product AXA has 16 elements among which are found
(-2.1), (1,2) and (3,1). Find the set A and the remaining elements of
ΑΧΑ.​

Answer 1

SOLUTION

GIVEN

The Cartesian product A × A has 16 elements among which are found(-2.1), (1,2) and (3,1).

TO DETERMINE

• The set A

• The remaining elements of Α × Α

CONCEPT TO BE IMPLEMENTED

CARTESIAN PRODUCT

Let A and B are two sets. Then the Cartesian product of A and B is denoted by A × B and defined as

A × B = { (x, y) : x ∈ A , y ∈ B }

In Cartesian product

n( A × B) = n(A) × n(B)

EVALUATION

Here it is given that , the Cartesian product

A × A has 16 elements

Therefore n( A × A ) = 16

∴ n(A) × n(A) = 16

∴ n(A) = 4

So A contains 4 elements

Now (-2, 1), (1,2) and (3,1) are the elements of A × A

So the elements of A are - 2 , 1 , 2 , 3

∴ A = { - 2 , 1 , 2 , 3 }

Now the all elements of A × A are (-2,-2), (-2,1),(-2,2),(-2,3),(1,-2),(1,1),(1,2),(1,3),(2,-2),(2,1),(2,2),(2,3),(3,-2),(3,1),(3,2),(3,3)

A × A = { (-2,-2), (-2,1),(-2,2),(-2,3),(1,-2),(1,1),(1,2),(1,3),(2,-2),(2,1),(2,2),(2,3),(3,-2),(3,1),(3,2),(3,3) }

Hence the elements of A × A other than (-2, 1), (1,2) and (3,1) are (-2,-2),(-2,2),(-2,3),(1,-2),(1,1),(1,3),(2,-2),(2,1),(2,2),(2,3),(3,-2),(3,2),(3,3)

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Answer 2

Step-by-step explanation:

please refer to the above attachment to your answer

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