Question

if set A={x:x is an isoscele triangle} and set B={x:x is an equilateral triangle} find intersection of A and B.

Answer 1

It is clear that
Isoceles triangle has 2 equal sides
Equilateral triangle has 3 equal sides.

Then each element of B is also an element of A.

Hence B is a proper subset of A.

Therefore

A intersection B = B

I hope this answer helps you

Answer 2

Hey There!!

Here we are given two sets:

A = {x : x  is an isosceles triangle}
B = {x : x is an equilateral triangle}


Let us first see the defintions of the two terms:

An Isosceles Triangle is a triangle that has two sides equal.

Note that this definition says that two sides must be equal. The third side may be equal, or may not be equal to the first two sites.


An Equilateral Triangle is a triangle with all three sides equal.


Here this definition makes it clear that all three sides must be equal. Only then can we call a triangle as an "equilateral triangle".


See the diagram for a better understanding.


Now, this makes one thing pretty clear. Since all equilateral triangles have three sides congruent (i.e. equal) they also have two sides equal.

This tells us that All equilateral triangles are isosceles triangles as well. However, All isosceles triangles are not equilateral triangles.



This means that Set B is subset of Set A.


$Since \, \, B \in A \\ \\ \\ \implies \boxed{A \cap B=B}$


Thus, intersection of Set A and Set B, is Set B, which becomes our answer.



Hope it helps
Purva
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