Showing posts with label Which of the following statements are incorrect and why. Show all posts
Showing posts with label Which of the following statements are incorrect and why. Show all posts

Tuesday, April 8, 2014

Which of the following statements are incorrect and why

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.