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Domain and Range of relations
βRβ is the relation from set P to set Q.
REMEMBER:
β’ The domain is the set of all the first components of the ordered pairs that belongs to R. Domain (R) = {π: (π, π) π π
}
β’ The range is the set of all the second components of the ordered pairs that belongs to R. Range (R) = {π: (π, π) π π
}
Worked Example 8
P Γ Q P = {1, 2, 3}, Q = {3, 2, 6}
R = {(1, 3), (1, 2), (1, 6), (2, 3), (2, 2), (2, 6), (3,3), (3, 2), (3, 6)} Domain (R) = {1, 2, 3}
Range (R) = {2, 3, 6}
Find the relation
, range and domain when
Solution:
Number of Relations from One Set to Another
The number of elements in Set P is r
The number of elements in Set Q is s
Number of elements in set (P Γ Q) = rs
Number of elements in subset of (P Γ Q) = 2rs
Therefore, number of relations possible from P to Q = 2rs
REMEMBER:
If n(P) = r n(Q) = s
n(P Γ Q) = rs
Number of relations possible from P to Q = 2rs
Inverse of a relation
For any relation R, the inverse of a relation is the interchanging of the first and second components of
-1 the given ordered pair. Itβs denoted by R .
R = {(1, 3), (1, 2), (1, 6)} R-1 = {(3, 1), (2, 1), (6, 1)}
Page 20 of 54
ALGEBRA
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