 # 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}} Ava-May Nelson 2021-02-27 Answered

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

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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
$a=2\in \left\{1,2,3\right\}$
Here, the element 2 belongs to the set $\left\{1,2,3\right\}$ thus the statement is true
consider statement
$b=\left\{2\right\}\in \left\{1,2,3\right\}$
Here the set {2} doesn't belong to the set $\left\{1,2,3\right\}$ thus the statement is false
consider statement
$c=2\subset \left\{1,2,3\right\}$
Here the number 2 is not the proper subset of $\left\{1,2,3\right\}.$
Thus the statement is false
consider he statement
$d=\left\{2\right\}\subset \left\{1,2,3\right\}$
Here the sett $\left\{2\right\}$ is proper subset of $\left\{1,2,3\right\}$
Thus the statements is true
consider the statement
$e=\left\{2\right\}\subset \left\{\left\{1\right\},\left\{2\right\}\right\}$
Here, the set $\left\{2\right\}$ is proper subset of $\left\{\left\{1\right\},\left\{2\right\}\right\}$ Thus, the statements is true
consider statement
$f=\left\{2\right\}\subset \left\{\left\{1\right\},\left\{2\right\}\right\}$ Here the set $\left\{2\right\}$ belongs tp $\left\{\left\{1\right\},\left\{2\right\}\right\}$.Thus the statement is true