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Let A ={1,2,{3,4},5}. Which of the follo...

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`.

Text Solution

AI Generated Solution

To determine which statements about the set \( A = \{1, 2, \{3, 4\}, 5\} \) are incorrect, we will analyze each statement one by one. ### Step-by-Step Solution: 1. **Statement (i):** `{3,4} ⊆ A` - **Analysis:** The statement claims that the set `{3, 4}` is a subset of \( A \). A subset means that every element of `{3, 4}` must be an element of \( A \). However, the elements `3` and `4` are not directly in \( A \); instead, they are contained within the set `{3, 4}` which is an element of \( A \). - **Conclusion:** This statement is **incorrect**. ...
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