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

Answer:

1. False
2. True
3. True
4. False.....

Answer 2

$\Huge{\bold{\mathrm{\underline{\red{ANSWER}}}}}$

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

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

(iii) False. 2ϵ{1,2,3}

However, 2∈/ {1,3,5}

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

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

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

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

Here, {2,4}⊂{1,2,3,4,6,9,12,18,36}