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

Asked by Pragya Singh | 11 months ago |  68

##### Solution :-

(i) Given,

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

To find if  {3, 4} ⊂ 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,

3 ∈ {3, 4}; however 3∉A

The given statement {3, 4} ⊂ A  is incorrect.

(ii) Given that,

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

To find if  {3, 4} ∈A is correct or incorrect.

From the above statement,

{3, 4} is an element of A.

{3, 4} ∈A

The given statement is correct.

(iii) Given that,

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

To find if {{3, 4}} ⊂ 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,

{3, 4} ∈ {{3, 4}} and {3, 4} ∈ A

{{3, 4}} ⊂ A

The given statement {{3, 4}} ⊂ A is correct.

(iv) Given that,

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

To find if 1∈ A is correct or incorrect.

From the above statement,

1 is an element of A.

The statement 1∈A is a correct statement.

(v)  Given that,

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

To find if 1⊂ 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,

An element of a set can never be a subset of itself. So $$1\nsubseteq A$$

The given statement 1⊂ A is incorrect statement.

Answered by Abhisek | 11 months ago

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