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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
What else can I help you with?
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.
How do you prove the pentagram angles inside a scalene pentagon equl 180?
To prove that the sum of the angles formed by the intersection of the diagonals within a scalene pentagon equals 180 degrees, you can use the fact that any polygon can be divided into triangles. In a pentagon, there are five sides, and thus it can be divided into three triangles by drawing diagonals. The interior angles of these triangles sum to 540 degrees, and since the angles at the vertices of the pentagon contribute to this sum, the angles formed by the intersection of the diagonals can be shown to sum to 180 degrees by subtracting the angles at the vertices from 540 degrees and considering the properties of linear pairs.
The intersection of the three medians of a triangle is called the?
centroid
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.
How do you prove the pentagram angles inside a scalene pentagon equl 180?
To prove that the sum of the angles formed by the intersection of the diagonals within a scalene pentagon equals 180 degrees, you can use the fact that any polygon can be divided into triangles. In a pentagon, there are five sides, and thus it can be divided into three triangles by drawing diagonals. The interior angles of these triangles sum to 540 degrees, and since the angles at the vertices of the pentagon contribute to this sum, the angles formed by the intersection of the diagonals can be shown to sum to 180 degrees by subtracting the angles at the vertices from 540 degrees and considering the properties of linear pairs.
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.
What is the intersection of three altitudes of a triangle called?
the orthocenter (:
The intersection of the three medians of a triangle is called?
centroid
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
