Mathematics
Given, A = {Triangles}, B = {Isosceles triangles}, C = {Equilateral triangles}. State whether the following are true or false. Give reasons.
(i) A ⊂ B
(ii) B ⊆ A
(iii) C ⊆ B
(iv) B ⊂ A
(v) C ⊂ A
(vi) C ⊆ B ⊆ A.
Sets
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Answer
A is a set which contains all triangles.
B is a set which contains all isosceles triangles.
C is a set which contains all equilateral triangles.
(i) False
Reason
As we know each triangle cannot be isosceles triangle.
Hence, A is not a proper subset of B.
(ii) True
Reason
As all isosceles triangles are type of triangles.
Hence, B is a subset of A.
(iii) True
Reason
As all equilateral triangles are isosceles triangles also.
Hence, C is a subset of B.
(iv) True
Reason
As all isosceles triangles are triangle also.
Hence, B is a proper subset of A.
(v) True
Reason
As all equilateral triangles are triangle also.
Hence, C is a proper subset of A.
(vi) True
Reason
As all equilateral triangles are isosceles triangle and all isosceles triangles are triangle also.
Hence, C is a subset of B and B is a subset of A.
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