What Are the Visual Representations of These Mathematical Subsets?

[mmathew23]

I haven't done mathematics in a while and I have this question to do.

Describe the following subests of the plane:

a. R x {1,2,4}
b. ([0,1] U [2,3]) x[0,1]
c. ([0,1] U [2,3]) x ([0,1]x[2,3])

2. I'm actually unsure of the relevant equations used for this sort of problem.

3. Basically I think the first one is the lines x=1, x=2, x=4, y=1, y=2, and y=4.
But in the back of my mind I think it's either only the y or the x equations. If someone could help me visualize this properly I think this problem would be much easier. Thanks.

 

[cristo]

Well the first one is a set of points such that the x value is any real number, and the y value is one of {1,2,4}. So, the first value for y gives $\{(x,y):x\in\mathbb{R}, y=1\}$. Can you identify this as one of the lines you suggest? Doing so for the other values of y will give you your solution.

For the other questions, think in the same way.

 

[Architeuthis Dux]

a. R x {1,2,4} represents the set of points on the real number line (R) that are paired with the elements 1, 2, and 4 from the set {1,2,4}. In other words, it is the set of points (x,y) where x is any real number and y can only be 1, 2, or 4. This can be visualized as three parallel lines on the plane, one at x=1, one at x=2, and one at x=4, with all possible y values at those points.

b. ([0,1] U [2,3]) x[0,1] represents the set of points on the plane that are within the closed intervals [0,1] or [2,3] on the x-axis, and within the closed interval [0,1] on the y-axis. This can be visualized as a rectangle with two smaller rectangles cut out of the corners, one at [0,1] on the x-axis and one at [2,3] on the x-axis.

c. ([0,1] U [2,3]) x ([0,1]x[2,3]) represents the set of points on the plane that are within the closed intervals [0,1] or [2,3] on the x-axis, and within the closed intervals [0,1] or [2,3] on the y-axis. This can be visualized as a larger rectangle with four smaller rectangles cut out of the corners, one at [0,1] on the x-axis and one at [2,3] on the x-axis, and two more at [0,1] and [2,3] on the y-axis.