Question

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}}f:{2}in{{1},{2}}

Discrete math
ANSWERED
asked 2021-02-27

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:\(\{2\}\in\{\{1\},\{2\}\}\)

Answers (1)

2021-02-28

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

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