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Q 01 / 25
A set is a well-defined collection of objects.
Q 02 / 25
The collection of all tall students in a class forms a set.
Q 03 / 25
The empty set contains no elements.
Q 04 / 25
The empty set is a subset of every set.
Q 05 / 25
If a set has n elements, then it has n subsets.
Q 06 / 25
If \(A = {1,2,3}\), then 2 ? A.
Q 07 / 25
If \(A = {1,2,3}\), then \({2} \in A\).
Q 08 / 25
Two sets are equal if they have the same number of elements.
Q 09 / 25
If A ? B and B ? A, then A = B.
Q 10 / 25
The universal set is always uniquely defined.
Q 11 / 25
The complement of a set A depends on the universal set.
Q 12 / 25
If A ? B, then \(A \cap B = A\).
Q 13 / 25
For any two sets A and B, \(A \cup B = B \cup A\).
Q 14 / 25
If \(A \cap B = \varnothing\), then A and B are equal sets.
Q 15 / 25
If A has 5 elements, then its power set has 32 elements.
Q 16 / 25
The power set of the empty set contains exactly one element.
Q 17 / 25
If \(A \cup B = A\), then B ? A.
Q 18 / 25
If \(A \cap B = A\), then A ? B.
Q 19 / 25
De Morgan’s law states \((A \cup B)' = A' \cup B'\).
Q 20 / 25
De Morgan’s laws hold for any number of sets.
Q 21 / 25
If A and B are finite sets, then \(n(A \cup B) = n(A) + n(B)\).
Q 22 / 25
If \(n(A)=n(B)=n(A\cap B)\), then A = B.
Q 23 / 25
If \(A \subset B\), then \(P(A) \subset P(B)\).
Q 24 / 25
If A has n elements, then the number of proper subsets of A is \(2^n - 1\).
Q 25 / 25
For finite sets A and B, if \(A \times B = B \times A\), then A = B.

Frequently Asked Questions

A set is a well-defined collection of distinct objects called elements.

So that it is possible to clearly decide whether a given object belongs to the set or not.

The individual objects or members contained in a set are called its elements.

Sets are generally denoted by capital letters such as \(A,\, B,\, C\).

Elements are represented by small letters such as \(a, \,b,\, x\).

It means “belongs to” or “is an element of”.

It means “does not belong to” a given set.

A method of listing all elements of a set within curly braces.

A representation describing a set by a common property satisfied by its elements.

(\A = {2,4,6,8}\).

\(A = {x : x \text{ is an even natural number}}\).

A set containing no elements, denoted by \(\varnothing\).

Yes, there is only one empty set.

A set containing exactly one element.

A set with a definite number of elements.
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