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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 PQ and R-P represents respectively?


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Solution

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

PQ= 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.)

RP= 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, PQ= set of all equilateral triangles and RP is the set of all non-isosceles right-angled triangles.


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