Answer with Step-by-step explanation:
We are given that A, B and C are subsets of universal set U.
We have to prove that
Proof:
Let x
Then and
When then
but
Therefore, but
Hence, it is true.
Conversely , Let but
Then and
When then
Therefor,
Hence, the statement is true.
Answers:
A diagram is shown below.
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Explanation:
First we locate point B at (4,3). The '4' in the x position means we've gone 4 units to the right of the origin, and the 3 in the y coordinate means we've gone 3 units up.
Now we need to find four points that are 8 units away from this central location. We'll ignore point A.
What we can do is add 8 to the x coordinate of point B to get x+8 = 4+8 = 12. Keeping the y coordinate the same, the point (12, 3) is exactly 8 units away from (4,3). Think of drawing a number line through those two points. Then we can note there are 8 spaces between (4,3) and (12,3). Or we can say "there are 8 spaces between 4 and 12" since that '3' doesn't really play much of a role in this case.
So (12,3) is one answer.
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Move back to point B(4,3)
Instead of adding 8 to the x coordinate, let's subtract 8 from it
x-8 = 4-8 = -4
Again the y coordinate is kept the same.
The point (-4, 3) is 8 units away from (4,3). The number line distance from -4 to 4 is 8 units.
So (-4,3) is another answer.
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Move back to point B
From this starting point, we can move 8 units up. Doing this means we add 8 to the y coordinate, while the x coordinate is kept intact.
(4,3) turns into (4,11) after doing so.
(4,11) is another answer.
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Move back to point B
From this point, we can move down 8 units to arrive at (4,-5). note how y-8 = 3-8 = -5. The x coordinate is kept the same.
(4,-5) is another answer.
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The four points we found were:
which are four possible answers
Those points are found by going 8 units right, 8 units left, 8 units up and 8 units down in that order. Each time we started at point B as our center of operation. The use of the word "center" is done because we can form a circle of radius 8, and the center of the circle is at B(4,3). Any point on the circle's edge is exactly 8 units away from the center point B.
Refer to the diagram below. The four answers are the red points P,Q,R,S. The point T is another point that could be an answer, but it's not as easy to find compared to the four other points.
