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

(i) {1, 2, 5} ⊂ A

(ii) {1, 2, 5} ∈ A

(iii) {1, 2, 3} ⊂ A

(iv) Φ ∈ A

(v) Φ ⊂ A

(vi) {Φ} ⊂ A

Asked by Pragya Singh | 1 year ago |  65

##### Solution :-

(i) Given that,

A = $$\{1,2,\{3,4\},5\}$$

To find if {1, 2, 5} ⊂ A is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

A⊂ B if a ∈ A,a ∈ B

From the above statement,

The each element of $$\{1,2,5\}$$ is also an element of A, So $$\{1,2,5\}$$⊂ A

The given statement $$\{1,2,5\}$$⊂ A is a correct statement

(ii) Given that,

A = $$\{1,2,\{3,4\},5\}$$

To find if $$\{1,2,5\}∈ A$$ A is correct or incorrect.

From the above statement,

Element of $$\{1,2,5\}$$ is not an element of A, So $$\{1,2,5\}∉ A$$

So the given statement $$\{1,2,5\}∈ A$$ is an incorrect statement.

(iii) Given that,

$$\{1,2,\{3,4\},5\}$$

To find if $$\{1,2,3\}⊂A$$  is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

A⊂ B if a ∈ A,a ∈ B

From the above statement, we notice that,

3 ∈ {1, 2, 3}; where, 3 ∉ A.

$$\{1,2,3\} \nsubseteq A$$

The given statement $$\{1,2,3\}⊂A$$ is an incorrect statement.

(iv) Given that,

$$\{1,2,\{3,4\},5\}$$

To find if Φ ∈ A is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

A⊂ B if a ∈ A,a ∈ B

From the above statement,

Φ is not an element of A. So, Φ ∈ A.

The given statement Φ ∈ A is an incorrect statement.

(v) Given that,

$$\{1,2,\{3,4\},5\}$$

To find if Φ ⊂ A is correct or incorrect

A set A is said to be a subset of B if every element of A is also an element of B

A⊂ B if a ∈ A,a ∈ B

From the above statement,

Since Φ is a subset of every set, Φ ⊂ A

The given statement Φ ⊂ A is a correct statement.

(vi) Given that,

$$\{1,2,\{3,4\},5\}$$

To find if {Φ} ⊂ A is correct or incorrect.

A set A is said to be a subset of B if every element of A is also an element of B

A⊂ B if a ∈ A,a ∈ B

From the above statement,

Φ is an element of A and it is not a subset of A.

The given statement {Φ} ⊂ A is an incorrect statement.

Answered by Abhisek | 1 year ago

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