Question

if A={-1, 1} and B{- 1,1} then geometrically describe the set of points of A×B. explain tat with notes​

Answer 1

Answer:

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Answer 2

SOLUTION

GIVEN

A = { - 1 , 1 } and B = { - 1 , 1 }

TO DETERMINE

Geometrically describe the set of points of A × B

CONCEPT TO BE IMPLEMENTED

Set :

A set is a well defined collection of distinct objects of our perception or of our thought to be conceived as a whole

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

$\sf{A \times B = \{(x, y) : x \in A \: \: and \: \: y \in B \}}$

EVALUATION

Here the given sets are

A = { - 1 , 1 } and B = { - 1 , 1 }

Now the Cartesian product of A and B is denoted by A × B and defined as

$\sf{A \times B = \{(x, y) : x \in A \: \: and \: \: y \in B \}}$

Thus

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

The set of points in A × B geometrically represents the points in two dimensional cartesian coordinate system

Figure : Figure is referred to the attachment

In the figure we draw the Cartesian coordinate system where A is along horizontal direction and B as vertical direction

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