Which of the following statements are true? Give reason to support your answer.
Which of the following statements are true? Give reason to support your answer.
(i) For any two sets $A$ and $B$ either $A \subseteq B$ or $B \subseteq A$;
(ii) Every subset of an infinite set is infinite;
(iii) Every subset of a finite set is finite;
(iv) Every set has a proper subset;
(v) {a, b, a, b, a, b, ...} is an infinite set;
(vi) {a, b, c} and {1, 2, 3} are equivalent sets;
(vii) A set can have infinitely many subsets.
(i) False
It is not necessary that for any two sets $A \& B$, either $A \subseteq B$ or $B \subseteq A$.
It is not satisfactory always.
Let:
$A=\{1,2\} \& B=\{\alpha, \beta, \gamma\}$
Here, neither $A \subseteq B$ nor $B \subseteq A$
(ii) False
$A=\{-1,0,1,2,3\}$ is a finite set that is a subset of infinite set $Z$.
(iii) True
$E$ very subset of a finite set is a finite set.
(iv) False
$\phi$ does not have a proper subset.
(v) False
$\{a, b, a, b, a, b, \ldots\}$ will be equal to $\{a, b\}$, which is a finite set.
(vi) True
$\{a, b, c\}$ and $\{1,2,3\}$ are equivalent sets because the number of elements in both the sets are same.
(vii) False
In the set $A=\{1,2\}$, subsets can be $\{\phi\},\{1\}$ and $\{2\}$, which are finite.