# Which of the following are true statements? 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}}

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:$$\{2\}\in\{\{1\},\{2\}\}$$

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Alannej

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