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If x and y and a be three non-empty sets such that a intersection x equals a intersection y and a union x equals a union y then prove that x equals y?
Let x, y, and a be sets and X,Y,x',y' be elements.
Denote X *x as X in (is an element of) x, I as intersection, and U as union.
If we can show that for all X *x, X *y (and similarly, if for all Y *y, Y *x), then we are done.
Case 1) xIa is empty
Then x, a and y, a have no elements in common. So, if xUa and yUa are equal, then for all y' *yUa but y' not*a, y' *y. Since xUa and yUa are equal, either y' *a or y' *x. But we supposed y' is not*a, so y'*x. Similarly, for all x' *x, x'*y. QED
Case 2) xIa is non-empty
Define a' as a - {x| x *xIa}. Then xIa' is empty, and you can use the same prove as above, replacing a with a'. QED
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What is the intersection of the medians called?
Intersection of Medians-Centroid Intersection of Altitudes-Orthocentre
What is the intersection of three or more edges?
A volume.
The intersection of the three medians of a triangle is called the?
centroid
The intersection of the three default reference planes?
The origin.
The intersection of the three medians of a triangle is called?
centroid
What is the intersection of the medians called?
Intersection of Medians-Centroid Intersection of Altitudes-Orthocentre
What is the intersection of the three altitudes of a triangle?
orthocenter
What is the intersection of the three altitudes in a triangle?
It is the orthocentre.
What is the intersection of three or more edges?
A volume.
Why can three coplanar lines have zero one two or three points of intersection?
If all three lines are parallel, there are zero points of intersection. If all three lines go through a point, there is one point of intersection. If two lines are parallel and the third one crosses them, there are two. If the three lines make a triangle, there are three points.
What is the intersection of the three medians of a triangle called?
centroid
The intersection of the three medians of a triangle is called the?
centroid
The intersection of the three default reference planes?
The origin.
The intersection of the three medians of a triangle is called?
centroid
What is the intersection of three altitudes of a triangle called?
the orthocenter (:
Prove that the sum of the measures of the three angles of every triangle is 180 degrees?
Angle a plus angle b subtract from 180 equals angle c
Why must the intersection of the three lines be the centre of gravity?
It need not be - it depends on what the three lines are!
