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 (vi) {1, 2, 5} ⊂ A (vii) {1, 2, 5} ∈ A (viii) {1, 2, 3} ⊂ A (ix) Φ ∈ A (x) Φ ⊂ A (xi) {Φ} ⊂ A

Answer 1

The given set is A={ 1,2,{ 3,4 },5 }.

(i)

It is given that { 3,4 }⊂A.

The given statement is incorrect because 3∈{ 3,4 }, but 3∉A.

(ii)

It is given that { 3,4 }∈A.

The given statement is correct because { 3,4 } is an element of A.

(iii)

It is given that { { 3,4 } }⊂A.

The given statement is correct because { 3,4 }∈{ { 3,4 } } and { 3,4 }∈A.

(iv)

It is given that 1∈A.

The given statement is correct because 1 is an element of A.

(v)

It is given that 1⊂A.

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

(vi)

It is given that { 1,2,5 }⊂A.

The given statement is correct because each element of { 1,2,5 } is also an element of A.

(vii)

It is given that { 1,2,5 }∈A.

The given statement is incorrect because { 1,2,5 } is not element of A.

(viii)

It is given that { 1,2,3 }⊂A.

The given statement is incorrect because 3∈{ 1,2,3 }, but 3∉A.

(ix)

It is given that ϕ∈A.

The given statement is correct because ϕ is a subset of every set.

(x)

It is given that ϕ⊂A.

The given statement is incorrect because ϕ∈{ ϕ }, but ϕ∉A.