Which of the following statements are incorrect and why

Tuesday, 8 April 2014
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
(i) Incorrect
3 and 4 are not element of set A. {3, 4} is an element of A. Hence, statement is incorrect.
(ii) Correct
{3, 4} is an element of A. Hence statement is correct.
(iii) Correct
{3, 4} is an element of A. So that {{3, 4}} will a subset of set A. Hence, statement is correct.
(iv) Correct
1 is an element of set A so that 1∈ A. Hence, statement is correct.
(v)Incorrect
1 is an element of set A so that {1} ⊂ A. Hence, statement is Incorrect.
(vi) Correct
1, 2 and 5 are element of set A so that {1, 2, 5} ⊂ A. Hence given statement is correct.
(vii) Incorrect
1, 2 and 5 are element of set A so that {1, 2, 5} ⊂ A. Hence given statement is incorrect.
(ix)Incorrect
Φ is not an element of set A. Hence the statement Φ ∈ A is incorrect.
(x)Correct
Empty set Φ is a subset of each and every set. Hence given statement Φ ⊂ A is always true.
(xi) Incorrect
Φ is not an element of set A. Hence the statement {Φ } ⊂ A is incorrect.

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