Solution: Subset | Sets and Functions - JEE PDF Download

-> Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces :

1. Since a student of  class XI of your school will obviously be the student of your school, 

{x : x is a student of Class XI of your school} ⊂ {x : x student of your school}

2. {x : x is an equilateral triangle in a plane} ⊂ {x : x is a triangle in the same plane}

3. {x : x is an even natural number}⊂{x : x is an integer}

4. φ ⊂{ 1, 3 }, where φ is an empty set. This is because empty set is the subset of every set.

-> Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

1. {3, 4} ⊂ A 

Just like 5 ∈ A but 5 ⊄ A, in the same way, {3,4} ∈ A but {3, 4} ⊄ A.

{3, 4} is an element of A, not the subset of it.

5. 1 ⊂ A 

1 is an element of set A, not the subset of it.

7. {1, 2, 5} ∈ A

Clearly, there is no {1, 2, 5} element in set A.

8. {1, 2, 3} ⊂ A

1, 2 are present in A, but 3 ∉ A, so {1, 2, 3} ⊄ A

9. φ ∈ A

Empty set is the subset of every set, but does not belong to a set.

11. {φ} ⊂ A

Clearly φ ⊂ A but {φ}  is not a subset of A.