Question

Give geometric representation for followings:
i) R x { 3}
ii) {1, 5) x ( 3, -2)

Answer 1

Step-by-step explanation:

The solution is in the attachment

Answer 2

(i) The geometric representation of R x {3} is y = 3.

We know that in an x-y coordinate plane the coordinates are denoted by
(x , y).
Here we have only the y coordinate which is equal to 3.
Hence, y = 3.
And R here denotes all the real values or the real numbers.
When we draw this graph, we will get a line parallel to x-axis.
As y = 3 is constant we will mark a coordinate (0,3) and draw a straight line from this coordinate.
This straight line will be parallel to x-axis and can extend up to infinity.
The coordinates of this line will always have a fixed value of y
which is y =3.
However, the value of x will keep on changing and can have several values up to infinity including all real numbers keeping y as constant.

(ii) The geometric representation of (1 , 5) x (3 , -2) equals a set of four coordinates.
When we are given two coordinates and we need to mark them on the cartesian plane.
We will find all the points corresponding those points.
(1 , 5) x (3 , -2) = { (1 , 3) , (1 , -2) , (5 , 3) , (5 , -2) }
Now we will mark all the points of this set on the cartesian plane.
(1 , 3) - Here, value of x = 1 and y = 3.
(1 , -2) - Here, value of x = 1 and y = -2.
(5 , 3) - Here, value of x = 5 and y = 3.
(5 , -2) - here, value of x = 5 and y = -2.

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