Question

If a and b are the line segment given by the intervals(-4,3)and(-2,3),represent the cartesian product of a and b

Answer 1

Answer:

1)  when intervals lie on same line then A×B = ( -12 , 9) .

2) when the intervals do not lie on same line

A×B = { (a,b) : a ∈ A ∧ b ∈ B } =  { (a,b) : a ∈ (-4 , 3)  ∧ b∈ (-2 ,3)  }

Step-by-step explanation:

IF the these intervals lie on the same line. Then

Let

A = (-4 , 3)

B = (-2 , 3)

Now

A×B = (-4 , 3) × (-2 , 3) = ( -12 , 9)

because

-4 × 3 = -12    which is the minimum value we get

 3 × 3 = 9.      which is the maximum value we get

IF the intervals do not lie on the same line then

In set building notation

A×B = { (a,b) : a ∈ A ∧ b ∈ B } =  { (a,b) : a ∈ (-4 , 3)  ∧ b ∈(-2 , 3) }

Answer 2

Answer:

Concept used:

Let A and B be two sets. Then the cartesian product of A and B is

denoted by AxB and is defined by

A x B = {(a,b) | a∈A and b∈B}

Given:

A=(-4,3)

B= (-2,3)

Then,

A x B ={(x,y) | x∈(-4,3) and y∈(-2,3)}

In geometrically A x B contains all the points of the interior of the

rectangle whose vertices are (-4,-2), (-4,3) (3,3) (3,-2)