Let A = \left \{ 1, 2, \left \{ 3, 4 \right \}, 5 \right \}. Which | Filo
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Class 11

Math

Co-ordinate Geometry

Sets

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Let . Which of the following statements are incorrect and why?
(i)  

(ii)  
(iii)
(iv)  
(v)  
(vi)
(vii)  
(viii)  
(ix)
(x) (xi)

Solution: Given

(i) The statement is incorrect because ; however, .

(ii) The statement is correct because is an element of A.

(iii) The statement is correct because and .

(iv) The statement is correct because 1 is an element of A.

(v) The statement is incorrect because an element of a set can never be a subset of itself.

(vi) The statement A is correct because each element of is also an element of A.

(vii) The statement is incorrect because is not an element of A.

(viii) The statement is incorrect because ; however, .

(ix) The statement is incorrect because is not an element of A.

(x) The statement is correct because is a subset of every set.

(xi) The statement is incorrect because ; however, .

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