Question

If P = Set of all triangles, Q = Set of scalene triangles, R = Set of isosceles triangles and

S = Set of equilateral triangles.
State which of the following statements are true or false.
(a) QCР
(b) RCS
(c) SCR
​

Answer 1

Given:

P = Set of all triangles,

Q = Set of scalene triangles,

R = Set of isosceles triangles and

S = Set of equilateral triangles.

To find:

Which of the following statements are true or false?

Solution:

We know that,

Scalene triangles : All sides are different.

Isosceles triangles : Two sides are equal.

equilateral triangles : All sides are equal.

Set of all triangles contains all scalene triangles. So, set of scalene triangles Q is a subset of Set of all triangles P.

`Q\subset P`

So, (a) is true.

All isosceles triangles are not equilateral triangles. So, set of isosceles triangles R is not a subset of set of equilateral triangles S.

`R\\subseteq S`

So, (b) is false.

Set of all isosceles triangles contains all equilateral triangles. So, set of equilateral triangles S is a subset of set of isosceles triangles R .

`S\subset R`

So, (c) is true.