Question

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}

Answer 1

(i) False. Each element of {a, b} is also an element of {b, c, a}.

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(ii) True. a, e are two vowels of the English alphabet.

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

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(iv) True. Each element of {a} is also an element of {a, b, c}.

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(v) False. The elements of {a, b, c} are a, b, c. Therefore, {a} {a, b, c}

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(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}