Question

What universal set(s) would you propose for each of the following?
(i) The set of right triangles
(ii) The set of isosceles triangles.

Answer 1

Hint: Here we use the definition of universal set and using the information that the universal set contains all the sets of possible outcomes we try to write the universal set for both options.
* Universal Set is denoted by U and it has all the elements of possible sets without repetition of the elements. So we can say all sets are contained in the Universal set.
* Right triangle is a triangle which has one angle as the right angle i.e. \[{90^ \circ }\]. The side opposite to the right angle is called hypotenuse and the vertical side of the triangle is called the perpendicular and the horizontal side of the triangle is called the base.
* An isosceles triangle is a triangle which has two sides equal to each other and two angles opposite to equal sides as equal.

Complete step-by-step answer:
We have to find universal set(s) for the two parts:
(i) The set of right triangles
We know that the right triangle is a form of triangle, so the universal set must contain all triangles.
Also, we know that in a polygon we can join vertices, after we join vertices different triangles are formed which might have a right triangle. Example: in a square, rectangle we join diagonals and we get right triangles.
So, we take all polygons in the universal set.
So, universal set is set of all triangles and set of all polygons.
(ii) The set of isosceles triangles
We know that isosceles triangle is a form of triangle, so the universal set must contain all triangles.
Also, we know that in a polygon we can join vertices, after we join vertices different triangles are formed which might have an isosceles triangle. Example: in a square we join diagonals and we get isosceles triangles because sides of the square are equal.
So, we take all polygons in the universal set.
So, universal set is set of all triangles and sets of all polygons.

Note: Students might not write the set of polygons in the universal set because they might think only the triangles should be in the universal set as we are taking sets of triangles. Keep in kind triangle is also a polygon, so we will take other polygons as well.