Let `A ={1,2,{3,4},5}`. Which of the following statements are incorrect and why ?
(i) `{3,4} subA`
(ii) `{3,4} in A`
(iii) `{{3,4}}sub A`
(iv) `1 in A`
(v) `1 sub A`
(vi) `{1,2,5} sub A`
(vii) `{1,2,5} in A`
(viii) `{1,2,3} sub A`
(ix) `phi in A`
(x) `phi sub A`
(xi) `{phi} sub A`.

Answer

(a),(e ) , (g) , (h) ,(i), (k) are incorrect

Explanation

We have set, A -' {1, 2, {3, 4}, 5}
(a) The statement {3, 4} `sub` A is incorrect because 3 `in` {3, 4}. however, `3 in A`.
(b) We know that the element of the set can be a set.
So, the statement {3, 4} `in A` is correct because {3, 4} is an element of A.
(c ) The statement {{ 3, 4}} ` in A` is correct because `{3, 4} in {{3, 4}} "and " {3, 4} in A.`
( d) The statement `1 in A` is correct because 1 is an element of A.
(e) The statement `1 sub A` is incorrect because an element of a set can never be a subset of the set.
(f) The statement `{1, 2, 5} sub A` is correct because each element of {1, 2, 5} is element of the set A
(g) The statement `{1, 2, 5} in A` is incorrect because set {1, 2, 5} is not an element of the set A.
(h) The statement `{1, 2, 3} sub A` is incorrect because `3 in {1, 2, 3 } ," however " 3 notin A`.
(i) The statement `phi in A` is incorrect because `(phi)` is a not an element of the set A.
(j) The statement `phi sub A` is correct because `phi ` is a subset of every set.
(k ) The statement `{phi} sub A` is incorrect because `phi in { phi}` however `phi notin A.`