Examine whether the following statements are true or false:
Question:

Examine whether the following statements are true or false:

Examine whether the following statements are true or false:

(i) {ab} ⊄ {bca}

(ii) {ae} ⊂ {xx is a vowel in the English alphabet}

(iii) {1, 2, 3} ⊂{1, 3, 5}

(iv) {a} ⊂ {abc}

(v) {a} ∈ (abc)

(vi) {xx is an even natural number less than 6} ⊂ {xx is a natural number which divides 36}

Solution:

(i) False. Each element of {ab} is also an element of {bca}.

(ii) True. ae are two vowels of the English alphabet.

(iii) False. 2∈{1, 2, 3}; however, 2∉{1, 3, 5}

(iv) True. Each element of {a} is also an element of {abc}.

(v) False. The elements of {abc} are abc. Therefore, {a}⊂{abc}

(vi) True. {x:x is an even natural number less than 6} = {2, 4}

{x:x is a natural number which divides 36}= {1, 2, 3, 4, 6, 9, 12, 18, 36}

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