State whether the following statements are true or false-i 1 -1-2-3ii a -b-c-aiii a -a-b-civ a-b - a-a-b-b-av The sets x-x - 8 - 8 is the null set-

(1) 1∈ (1,2,3) yes, 1 is an element of the set {1,2,3} (2)a⊂{b,c,a} yes ,a is a subset of {b,c,a} (3) a∈{a,b,c} yes,a is an eleme ...

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Standard XII

Mathematics

Definition of Sets

State whether...

Question

State whether the following statements are true or false:
i) $1 \in {1, 2, 3}$
ii) $a \subset {b, c, a}$
iii) ${a} \in {a, b, c}$
iv) ${a, b} = {a, a, b, b, a}$
v) The sets ${x : x + 8 = 8}$ is the null set.

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Solution

$(1) 1 \in (1, 2, 3)$
yes, $1$ is an element of the set ${1, 2, 3}$
$(2) a \subset {b, c, a}$
yes ,a is a subset of ${b, c, a}$
$(3) a \in {a, b, c}$
yes,a is an element of ${a, b, c}$
$(4) {a, b} = {a, a, b, b, a}$
yes, the following statement is true.
$(5) {0}$
The set is not a null set the statement is False.

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Similar questions

Q. State whether the following statements are true or false:
(i)

1 \in \{1, 2, 3\}

(ii)

a \subset {b, c, a}

(iii)

\{a\} \in \{a, b, c\}

(iv)

\{a, b\} = \{a, a, b, b, a\}

(v) The set {x ; x + 8 = 8} is the null set.

Q. Examine whether the following statements are true or false:
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(iv) {

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(v) {

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ϵ

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}
(vi) {

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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}

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Q. Which of the following statements are true? Give reason to support your answer.
(i) For any two sets A and B either

A \subseteq B or B \subseteq A;

(ii) Every subset of an infinite set is infinite;
(iii) Every subset of a finite set is finite;
(iv) Every set has a proper subset;
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Which of the following statements are true ? Give reason to support your answer.

(i) For any two sets A and B either A $\subseteq$ B or B $\subseteq$ A.

(ii) Every subset of an infinite set is infinite.

(iii) Every subset of a finite set is finite.

(iv) Every set has a proper subset.

(v) {a,b,a,b,a,b....} is an infinite set.

(vi) {a, b, c} and {1, 2, 3} are equivalent sets.

(vii) A set can have infinitely many subsets.

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State whether the following statements are true or false:i) 1∈{1,2,3}ii) a⊂{b,c,a}iii) {a}∈{a,b,c}iv) {a,b}={a,a,b,b,a}v) The sets {x:x+8=8} is the null set.

(1)1∈(1,2,3)yes, 1 is an element of the set {1,2,3}(2)a⊂{b,c,a}yes ,a is a subset of {b,c,a}(3)a∈{a,b,c}yes,a is an element of {a,b,c}(4){a,b}={a,a,b,b,a}yes, the following statement is true.(5){0}The set is not a null set the statement is False.

State whether the following statements are true or false:
i) $1 \in {1, 2, 3}$
ii) $a \subset {b, c, a}$
iii) ${a} \in {a, b, c}$
iv) ${a, b} = {a, a, b, b, a}$
v) The sets ${x : x + 8 = 8}$ is the null set.