## Let f: AB be a function defined by f(2)=2x-1 where A={2,4,6,10,12) , B = {3,7; 11,19,23,25) Represent F by i) set of ordered

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## Answers ( )

Answer: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}

If A = {1, 2, 3} and B = {4, 5}, then

A × B = {(1, 4), (2, 4), (3, 4), (1, 5), (2, 5), (3, 5)}

and B × 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), (

1

2

, 3)} is a relation; the domain of

R = {1, – 2,

1

2

} and the range of R = {2, 3}.

Step-by-step explanation: