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Sets (VARIOUS TYPES OF SETS (Comparable and Incomparable Sets (Two sets A…
Sets
VARIOUS TYPES OF SETS
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Family of Sets
If a set A contains elements which are itself sets then it is called family of sets or a set of sets
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Subset of a Set
If every element of a set A is also an element of a set B then A is called subset of B and is written as A ⊆ B. B is called superset of A.
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Improper Subset. If A is subset of B and A = B, then A is said to be an improper subset of B
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Power Set
power set of any given set A is the set of all subsets of A and is denoted by P(A). If A has n elements then P(A) has 2n elements
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Universal Set
f all the sets under investigation are subsets of a fixed set U, then the set U is called universal set
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VENN DIAGRAMS
Venn diagram to represent the sets A, Ac and U
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STANDARD NOTATIONS
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C, C0 The sets of all complex, non-zero complex numbers respectively.
Q, Q0, Q+ The sets of rational, non-zero rational, + ve rational numbers respectively.
R, R0, R+ The sets of real, non-zero real, +ve real number respectively.
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MULTISETS
A multiset is an unordered collection of elements, in which the multiplicity of an element may be one or more than one or zero
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ORDERED PAIRS
two elements designated 1st member and 2nd member written as (p, q).
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