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

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

Text Solution

AI Generated Solution

To determine which statements about the set \( A = \{1, 2, \{3, 4\}, 5\} \) are incorrect, we will evaluate each statement one by one. ### Step-by-Step Solution: 1. **Statement (i):** \(\{3, 4\} \subset A\) - **Evaluation:** This statement is incorrect. The set \(\{3, 4\}\) is not a subset of \(A\) because \(\{3, 4\}\) is an element of \(A\), not individual elements. For \(\{3, 4\}\) to be a subset, both 3 and 4 must be elements of \(A\), which they are not. - **Conclusion:** Incorrect. ...
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