Q.Number of proper subsets of a set having 5 elements are :

The novels written by Munshi Prem Chand form a finite set, since he wrote a definite, countable number of novels during his lifetime.

A set is a well-defined collection of objects. 'Novels written by Munshi Prem Chand' is well-defined because for any given novel, we can definitely say whether it was written by him or not. Since Prem Chand wrote his novels over a finite lifetime, the total …

Sets with no element in common are disjoint sets, $A\cap B=\varnothing$.

When no element of $A$ belongs to $B$ and no element of $B$ belongs to $A$, the two sets share nothing, so their intersection is empty: $A\cap B=\varnothing$. Such sets are disjoint.

• Empty set — a set with no elements (not about two sets).
• Equal sets — exactly the same elements. …

One-word term: Empty set (null set), $\varnothing$.

A set having no elements at all is the empty set, written $\varnothing$ or $\{\,\}$. It is also called the null set or void set, and it …

Total subsets $=2^5=32$; removing the set itself leaves $31$ proper subsets.

Step 1 — a set with $n$ elements has $2^{n}$ subsets. Here $n=5$:

$2^{5}=32$

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The set of all elements under study is the universal set.

In set theory, the universal set (denoted $U$ or $\xi$) is the set that contains all the elements under consideration for a particular discussion; every other set in that context is a subse …

Only the integer 0 lies in $[-1/2, 1/2]$, so $A$ has exactly one element.

We need integers $x$ satisfying $-\dfrac{1}{2} \le x \le \dfrac{1}{2}$.

The only integer in this range is $x = 0$ (since $-1/2 = -0.5$ and $1/2 = 0.5$, and there is no other integer strictly between them or equal to them).

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Empty set $=\{\ \}=\varnothing$, with $n(\varnothing)=0$.

A null (empty) set is the set containing no elements, written $\{\ \}$ or $\varnothing$.

• $\{0\}$ has one element (the number $0$), so it is not empty. …

$2^n$ subsets with $n=5$ gives $32$.

For a set with $n$ elements, each element may independently be in or out of a subset, giving

$2^n \text{ subsets}.$

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A = {x : x is a prime number} has no last element, so it is infinite.

A set is finite if counting its elements terminates at a definite number; otherwise it is infinite.

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The term is the Empty set (null set), denoted $\varnothing$ or $\{\,\}$.

A set that contains no elements is called the empty set, null set or void set, and is written as $\varnothing$ or $\{\,\}$. Its cardinality is $n(\varnothing) = 0$, e.g. the set of natural numbers between $2$ and $3$ is empty. Note …