Mathematics
Given, A = {Quadrilaterals}, B = {Rectangles}, C = {Squares} and D = {Rhombuses}. State, giving reasons, whether the following are true or false.
(i) B ⊂ C
(ii) D ⊂ B
(iii) C ⊆ B ⊆ A
(iv) D ⊂ A
(v) B ⊇ C
(vi) A ⊇ B ⊇ D
Sets
3 Likes
Answer
A is set of all quadrilaterals.
B is set of all rectangles.
C is set of all squares.
D is set of all rhombuses.
(i) False
Reason
As all rectangles are not squares.
Hence, B is a not proper subset of C.
(ii) False
Reason
As all rhombuses are not rectangles.
Hence, D is a not proper subset of B.
(iii) True
Reason
As all squares are rectangles and all rectangles are quadrilateral.
Hence, C is a subset of B and B is a subset of A.
(iv) True
Reason
As all rhombuses are quadrilateral.
Hence, D is a proper subset of A.
(v) True
Reason
As all squares are rectangles.
Hence, C is a subset of B.
(vi) False
Reason
As all rectangles are quadrilateral but all rhombuses are not rectangles.
Hence, B is a subset of A and D is not a subset of B.
Answered By
2 Likes
Related Questions
Find the proper subsets of {x : x2 - 9x - 10 = 0}.
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.
Given, universal set = {x : x ∈ N, 10 ≤ x ≤ 35}, A = {x ∈ N : x ≤ 16} and B = {x : x > 29}. Find:
(i) A'
(ii) B'
Given, universal set = {x ∈ Z : - 6 < x ≤ 6}, N = {n : n is a non-negative number} and P = {x : x is a non-positive number}. Find :
(i) N'
(ii) P'