Question

Let $S=$ the set of all triangles,$P=$ the set of all isosceles triangles, $Q=$ the set of all equilateral triangles, $R=$ and the set of all right-angled triangles. What do the sets $P\cap Q$ and $R-P$ represents respectively?

Answer 1

Identifying the representation of the given sets:

Given that $S=$ the set of all triangles

$P=$ the set of all isosceles triangles

$Q=$ the set of all equilateral triangles

$R=$ the set of all right-angled triangles

$P\cap Q=$ set of all equilateral triangles. (because the isosceles triangles have 2 sides equal, and the equilateral triangle has all sides equal. Their two sides are also equal. So, all equilateral triangles are isosceles.)

$R–P=$ set of all non-isosceles right-angled triangles.

Right-angled triangle can be isosceles or non-isosceles. On subtracting the set of the isosceles triangle from $R$. We are left with the right-angled triangle which is not isosceles.

Therefore, $P\cap Q=$ set of all equilateral triangles and $R–P$ is the set of all non-isosceles right-angled triangles.