A. Describe the universal set and subset shown in the figure below Universal set Subset
1 answer:
Set theory is the mathematical study of sets, which are well defined object collections
The description of the universal set and subset are as follows;
Universal set: = {x ∈ N | 0 < x < 8} = { 1, 2, 3, 4, 5, 6, 7}
Subset: Set A = {x ∈ N | 0 < x < 8, x is odd} = {2, 4, 6 }
The reason the above values are correct are as follows;
The universal set, is the set containing without repetition the elements of all sets that is related to it
From the diagram in the question, we have;
Universal set:
The universal set has all elements in the rectangular enclosed area, which are natural numbers, <em>N</em>, larger than 0, but less than 8
Therefore, we have;
- Universal set:
= {<u>1, 2, 3, 4, 5, 6, 7</u>}, which is the set of natural numbers between 1 and 7
∪ = {x ∈ N | 0 < x < 8}
Subset:
A set <em>A</em> which is a subset of a set <em>B</em> is such that all the set <em>B</em> has all the elements of the set <em>A</em>
A subset is given by the set of elements enclosed in the circular area, which is a located within in the rectangular figure representing the universal set and , which is the set of all even natural numbers, <em>N</em>, larger than 0, but less than 8
Therefore, we have;
- Subset: Set A = {<u>2, 4, 6</u> }, which is the set of even numbers between 1 and 7
A = {x ∈ N | 0 < x < 8, x is odd}
Learn more about about set theory here:
You might be interested in
Answer:
1) The inequality for the given system are
y ≥ 4x - 4
y ≥ x - 1.5
2) The test point (0,0) satisfies both of the inequalities in the system represented by the graph.
Step-by-step explanation:
Given : A graph showing a system of inequalities.
We have to find the system of inequality.
For line 1)
The points that cut the x and y axis are (1,0) and (0,-4)
Thus, we can find the equation of line using two given point.
Since the general equation of line is y = mx + c
Where m is slope and c is y intercept
Slope is find as
Substitute, we get,
Slope is 4.
Thus, equation becomes y = 4x + c
For c put (0,-4) in the above equation , we have,
-4 = 4(0) + c ⇒ c = -4
Thus, equation becomes y = 4x - 4
For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region
For (0,0)
y = 4x - 4 becomes 0 = - 4 is satisfied when 0 > -4
thus, the inequality becomes y ≥ 4x - 4
Since, the line is a solid so it will take up equality sign too.
For line 2)
The points that cut the x and y axis are (1.5,0) and (0,-1.5)
Thus, we can find the equation of line using two given point.
Since the general equation of line is y = mx + c
Where m is slope and c is y intercept
Slope is find as
Substitute, we get,
Slope is 1.
Thus, equation becomes y = x + c
For c put (0,-1.5) in the above equation , we have,
-1.5 = (0) + c ⇒ c = - 1.5
Thus, equation becomes y = x - 1.5
For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region
For (0,0)
y = x - 1.5 becomes 0 = -1.5 is satisfied when 0 > - 1.5
thus, the inequality becomes y ≥ x - 1.5
Since, the line is a solid so it will take up equality sign too.
Thus, the inequality for the given system are
y ≥ 4x - 4
y ≥ x - 1.5
Also, The test point (0,0) satisfies both of the inequalities in the system represented by the graph.
