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Represent the function f = {(1,2),(2,2),(3, 2),(4,3),(5,4)} through
(ii) a table form
(i) an arrow diagram
(iii) a graph
function
Answers
Definition : Given two non-empty sets A and B, the set of all ordered pairs (x, y), where x ∈ A and y ∈ B is called Cartesian product of A and B; symbolically, we write
A × B = {(x, y) | x ∈ A and y ∈ B} IfA = {1, 2, 3} and B = {4, 5}, then
A × B = {(1, 4), (2, 4), (3, 4), (1, 5), (2, 5), (3, 5)} andB × A = {(4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3)}
(i)Two ordered pairs are equal, if and only if the corresponding first elements are equal and the second elements are also equal, i.e. (x, y) = (u, v) if and only if x = u, y = v.
(ii)If n(A) = p and n (B) = q, then n (A × B) = p × q.
(iii) A × A × A = {(a, b, c) : a, b, c ∈ A}. Here (a, b, c) is called an ordered triplet.
2.1.2 Relations A Relation R from a non-empty set A to a non empty set B is a subset of the Cartesian product set A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
The set of all first elements in a relation R, is called the domain of the relation R, and the set of all second elements called images, is called the range of R.
For example, the set R = {(1, 2), (– 2, 3), ( 12 , 3)} is a relation; the domain of
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R = {1, – 2, 12 } and the range of R = {2, 3}.
Answer:
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