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A Knowledge Hub by Rahul Anand
Mathematical Marvels: Insights from the Field
Venn Diagrams in Sets
Venn diagrams are the pictorial or graphical representation of sets and the various relationships that exist between sets. The representation consists of a rectangular box representing the universal set(U). All sets that are in context are drawn as circles…
UNIVERSAL SET
When working with sets, a reference superset that contains all the sets and their subsets in context (i.e. the sets which are currently under consideration) is called a universal set. It provides a base set from which all of the sets of interest can be…
Partitions
Partitioning of a set is distributing the member elements of a set among a group of non-empty subsets in such a way that each member lies in only one of these subsets. ⇒ ∅ ( Empty Set ) cannot be the partition of any set. Examples ⇒ The set { 1, 2, 3 } can be…
Disjoint Sets
Two sets A and B are called disjoint when they have no element in common (except the empty set ∅ }.
Power Set
The set of all possible subsets of a set S is called the power set of S, written as P(S). Examples ⇒ The power set of { ‘a’ } is { ∅, {‘a’} }The power set of { 2, 3 } is { ∅, {2}, {3}, {2,3} }The power set of {1, 2, 3 } is { ∅, {1}, {2}, {3}, {1,2}, {1,3}, {2,3},…
Proper Subset
If A is a subset of B but A ≠ B, then A is called the proper subset of B, and B is called the proper superset of A. This relationship is represented as below A ⊂ B ( A is a proper subset of A )B ⊃ A ( B is a proper superset of A ) Examples ⇒ {…
Subset
If there are two sets A & B such that every element of A is also in B, then A is called a subset of B. In other words, A is contained in B. B is called the superset of A. In the set theory, this relationship is depicted as below…
Equivalent Sets
Two sets A and B are said to be equivalent(≡) if each element of A is also an element of B and each element of B is also an element of A. If elements are repetitive in one set, then it is not required for it to repeat in the other set for the two sets to be…
Calculus Castle
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Insight into the Laws of Physics
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NUMERICAL SOLUTIONS IN PHYSICS
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Atom to Atom: Insights from the Chemical Universe
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Life’s Mysteries Revealed: Exploring Biology
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