You visited us 1 times! Enjoying our articles? Unlock Full Access!

Cardinal Properties

Examine wheth...

Question

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

Open in App

Solution

(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. $2 ϵ {1, 2, 3}$
However, $2 \notin {1, 3, 5}$
(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, $a \subset a, b, c$
(vi) True. ${x : x is an even natural number less than 6} = {2, 4}$
${x : x is a natural number which divides 36} = {1, 2, 3, 4, 6, 9, 12, 18, 36}$
Here, ${2, 4} \subset {1, 2, 3, 4, 6, 9, 12, 18, 36}$

Suggest Corrections

Similar questions

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}

(i) {a, b} \subset̸ {b, c, a}

(i i) {a, e} \subset {x : x

}

(i i i) {1, 2, 3} \subset {1, 3, 5}

(i v) {a} \subset {a, b, c}

(v) {a} \in {a, b, c}

(v i) {x : x

6} \subset {x : x

36}

Examine whether the following statements are true or false :

(i) {a, b} $\subset̸$ {b, c, a}

(ii) {a, e} $\subset$ {x: x is a vowel in the English alphabet}

(iii) {1, 2, 3} $\subset$ {1, 3, 5}

(iv) {a} $\subset$ {a, b, c}

(v) {a} $\in$ {a, b, c}

(vi) {x : x is an even natural number less than 6} $\subset$ {x : x is a natural number which divides 36}

1, 3, 5

1, 2, 3

a, e, i, o, u

a, b, c

x : x

3

x : x

6

1 < x \leq 6

B = ϕ

Join BYJU'S Learning Program