Question

What universal set (s) would you propose for the following: The set of right triangles.

Answer 1

Hint: To find the universal set of right angled triangles, we will try to find all the possible triangle families or polygons which are under consideration.

Complete step-by-step answer:
It is given in the question that we have to find the universal set of right angled triangles. Before we proceed with the question, let us first see what a universal set means. A universal set is a set which has all the elements under consideration, it is generally denoted by a capital letter. All other sets are subsets of the universal set.
For example, let us consider a set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} as S and let another set A = {1, 3, 5, 7, 9} and let set B = {2, 4, 6, 8, 10}. Here we can say that, S is the universal set as it contains all the elements of sets A and B. And also we can say that sets A and B are subsets of set S.
Generally, subset is denoted by $'\subseteq '$. So, we can write A $\subseteq $ S and also B $\subseteq $ S.
When we represent A, B and S in the Venn diagram, it can be shown as below.

So, if we consider the right angled triangle, then it is a type of triangle and there are also many other triangles possible. So, if we consider all the possible triangles, then we get the universal set of a right angle triangle as a set of triangles or a set of polygons, as a triangle is a polygon having three sides.
Therefore, for the set of triangles, the universal set is the set of triangles or the set of polygons.

Note: Students must know the basic concept of sets, only then they will be able to solve the questions without any mistakes. It must be understood that the universal set is a set containing all the possible elements of a particular group and that it can contain many subsets.