Which of following are true? a:2in{1,2,3}b:{2}in{1,2,3}c:2sube{1,2,3}d:{2}sube{1,2,3}e:{2}sube{{1},{2}}

Question

Which of the following are true statements?
a: $2 \in {1, 2, 3}$
b: ${2} \in {1, 2, 3}$
c: $2 \subset {1, 2, 3}$
d: ${2} \subset {1, 2, 3}$
e: ${2} \subset {{1}, {2}}$
f: ${2} \in {{1}, {2}}$

Answer 1

Definition used:
Proper subset: A proper subset of a set A is a subset of A that is not equal to A.
The element x belongs to the set A means the element in the set A.
Consider statement
$a = 2 \in {1, 2, 3}$
Here, the element 2 belongs to the set ${1, 2, 3}$ thus the statement is true
consider statement
$b = {2} \in {1, 2, 3}$
Here the set {2} doesn't belong to the set ${1, 2, 3}$ thus the statement is false
consider statement
$c = 2 \subset {1, 2, 3}$
Here the number 2 is not the proper subset of ${1, 2, 3} .$
Thus the statement is false
consider he statement
$d = {2} \subset {1, 2, 3}$
Here the sett ${2}$ is proper subset of ${1, 2, 3}$
Thus the statements is true
consider the statement
$e = {2} \subset {{1}, {2}}$
Here, the set ${2}$ is proper subset of ${{1}, {2}}$ Thus, the statements is true
consider statement
$f = {2} \subset {{1}, {2}}$ Here the set ${2}$ belongs tp ${{1}, {2}}$ .Thus the statement is true

Which of following are true? a:2in{1,2,3}b:{2}in{1,2,3}c:2sube{1,2,3}d:{2}sube{1,2,3}e:{2}sube{{1},{2}}

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