Whats the difference between a subset and a proper subset? {5,8} {2,5,8} Is {5,8} a subset of {2,5,8}.
1 answer:
Answer:
is a subset of
Step-by-step explanation:
Required
Difference between subset and proper subset
To answer this question, I will use the following illustration.
In the above sets, set B is a proper subset of set A because all elements of B can be found in A, but not element of A can be found in B.
Set C is a subset of A because
Using the above illustration, we have:
and
is a subset of
, because 5 and 8 are in
but 2 which ca be found in
is not in
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Answer:
Estimations of π/4:
100 points: 0.75
1,000 points: 0.768
10,000 points: 0.7819
Step-by-step explanation:
To get an estimate of π/4 you can place random points in the square [0, 1] × [0, 1] and estimate it as the ratio of the points that landed inside the unit circle to the total number of points (because the ratio of the area of the circle to the area of the square is π/4).
We do it for 100 xy points and we get:
Point inside the circle area = 75
Estimation of π/4 = 0.75
We do it for 1,000 xy points and we get:
Point inside the circle area = 768
Estimation of π/4 = 0.768
If we do it fo 10,000 xy points, we get
Point inside the circle area = 768
Estimation of π/4 = 0.768
The value of π/4 (4 decimals) is 0.7854.
The simulation gets more precise with the increase in the number of points.
The spreadsheet and the graphs are attached.
