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=2in{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=2sube{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}sube{1,2,3}

Here the sett {2} is proper subset of {1,2,3}

Thus the statements is true

consider the statement

e={2}sube{{1},{2}}

Here, the set {2} is proper subset of {{1},{2}} Thus, the statements is true

consider statement

f={2}sube{{1},{2}} Here the set {2} belongs tp {{1},{2}}.Thus the statement is true

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=2in{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=2sube{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}sube{1,2,3}

Here the sett {2} is proper subset of {1,2,3}

Thus the statements is true

consider the statement

e={2}sube{{1},{2}}

Here, the set {2} is proper subset of {{1},{2}} Thus, the statements is true

consider statement

f={2}sube{{1},{2}} Here the set {2} belongs tp {{1},{2}}.Thus the statement is true