Question

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

(i) {3,4} ⊂ A

(ii) {3,4} ∈ A

(iii) {{3,4}} ⊂ A

(iv) 1 ∈ A

(v) 1 ∈ A

(vii) {1, 2, 5} ⊂ A

(ix) Φ ⊂ A

(xi) {Φ} ⊂ A

Answer 1

(i) (3,4} c A

This statement is not correct because {3, 4} is element of set^4. Thus, {{3,4}} czA.

Hence, 1 ∈ A, 2 ∈ A, {3,4} ∈ A, 5 ∈ A all these are elements of A.

(ii) (3,4} ∈ A is true because set {3, 4} is element of A.

(iii) {{3, A}}⊂ A is true because {3, 4} is element of set A when we write {{3, 4}} then it becomes set.

Thus, {{3,4}} ⊂ A.

(iv) 1 ∈ A is true because lis element of set A.

(v) 1 ⊂ A is not true because any element cannot be subset of any set until it is written in {} bracket.

(vi) {1, 2, 5} ⊂A is true because {1, 2, 5} is set of elements 1,2,5 of A.

(vii) {1, 2, 5} ∈ A is not true because 1, 2, 5 are elements of set A. Thus, {1,2,5} will be subset of set A.

(viii) {1, 2, 3} ⊂ A is not true because 3 is not an element of set A.

(ix) Φ ∈ A is not true because f .is not elements of set A.

(x) Φ ⊂ A is true because null set Φ is subset of all sets.

(xi) {Φ} ⊂ A is not true because Φ is null set and Φ is element of set {Φ}.