Where Exploration Leads to Academic Excellence
A Knowledge Hub by Rahul Anand
Mathematical Marvels: Insights from the Field
Ordered Pairs
An ordered pair is a 2-tuple formed by taking two elements (generally numbers but can be alphabets, characters, words, or symbols). The general form of representation is (a, b) where a and b represent two distinct objects. The important thing with ordered pairs is…
Cartesian Product
The cartesian product of two sets A and B is defined as a set formed by all the possible ordered pairs of elements from A and B, such that the first element comes from set A and the second element comes from set B. The cartesian product is denoted as A × B….
Intersection operation on two sets
The intersection of two sets A & B is defined as a set that contains only those members which are common to both A and B. The intersection operation is denoted by the symbol ∩. Remember, for two disjoint sets (sets having no common elements), the…
Union of two sets
The union of two sets A & B is defined as a set that contains all the member elements of A and B. the union operation is denoted by the symbol ∪. One point to remember here is that the union of two or more sets always gives a set with distinct…
Complement of a set
The complement of a set A (that is a subset of a universal set U) is defined as a set that contains all the member elements and all subsets of U that are not part of the set A. The complement of a set is denoted using the symbol ‘ or c. Hence, A’ =…
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…
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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