QuestionDraw a Venn diagram for sets of triangles: equilateral , isosceles , right-angled . Describe their unions and intersections.
Studdy Solution
STEP 1
Assumptions1. We have three sets (equilateral triangles), I (isosceles triangles), and R (right-angled triangles).
. The universal set is the set of all triangles.
3. The sets may have intersections, meaning that a triangle could belong to more than one set. For example, an isosceles triangle could also be a right-angled triangle.
STEP 2
To draw a Venn diagram for the sets, I and R, we first draw a rectangle to represent the universal set of all triangles. Inside this rectangle, we draw three circles that overlap each other, representing the sets, I and R.
STEP 3
The Venn diagram should look like this\begin{array}{c} \text { Universal set (All triangles) } \\ \includegraphics[width=0.5\textwidth]{venn_diagram.png} \\ \text { Equilateral triangles, I Isosceles triangles, R Right-angled triangles } \end{array}
STEP 4
To sketch a member of I R, we need to draw a triangle that is both isosceles and right-angled. This is a triangle with two sides of equal length and one angle of90 degrees.
STEP 5
The set represents all triangles that are either isosceles or equilateral. This includes all equilateral triangles (which are also isosceles), and all isosceles triangles that are not equilateral.
STEP 6
The set represents all triangles that are either isosceles or right-angled. This includes all isosceles right-angled triangles, and all other isosceles and right-angled triangles.
STEP 7
The set represents all triangles that are both isosceles and equilateral. Since all equilateral triangles are also isosceles, this set is the same as the set of all equilateral triangles.
STEP 8
The set represents all triangles that are both equilateral and right-angled. However, it is impossible for a triangle to be both equilateral and right-angled, so this set is empty.
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