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Examine whether the following statements...

Examine whether the following statements are true or false:
(i) { a, b } ⊄ { b , c, a }
(ii) { a , e } ⊂ { x : x is a vowel in the English alphabet}
(iii) { 1, 2, 3 } ⊂ { 1, 3, 5 }
(iv) { a }⊂ { a, b, c }
(v) { a }∈ { a , b, c }
(vi) { x : x is an even natural number less than 6} ⊂ { x : x is a natural number which divides 36}

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To determine whether the given statements are true or false, we will analyze each statement step by step. ### Step-by-Step Solution: **(i)** **Statement:** { a, b } ⊄ { b, c, a } **Analysis:** The notation ⊄ means "is not a subset of." A set A is a subset of set B if every element of A is also an element of B. Here, both elements 'a' and 'b' from the first set { a, b } are present in the second set { b, c, a }. Therefore, { a, b } is indeed a subset of { b, c, a }. **Conclusion:** This statement is **False**. ...
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