Question

Let A={all quadrilaterals}, B={all rectangles}, C={all squares} and D={all rhombuses} in a plane. State, giving reasons, whether the following statements are true or false:

i) B is proper subset of C is proper subset of A

ii) C is proper subset of B is proper subset of A

iii) C is proper subset of D is proper subset of A

iv) D is proper subset of C and is proper subset of A

Answer 1

Given, A={all quadrilaterals}, B={all rectangles}, C={all squares} and D={all rhombuses}

i) B is proper subset of C is proper subset of A : - false

It is false due to the fact that all squares are rectangles and not every rectangle is a square.

ii) C is proper subset of B is proper subset of A :- True

It is true due to the fact that all squares are rectangles and not every rectangle is a square.

iii) C is proper subset of D is proper subset of A :- True

It is true due to the fact that all squares are rhombuses and not every rhombus is a square.

iv) D is proper subset of C and is proper subset of A : False

It is false due to the fact that all squares are rhombuses and not every rhombus is a square.