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Ordered Pair

Use the eleme...

Question

Use the elements of set A ={x, y, z} to form all possible ordered pairs.
Find the number of elements in the ordered pair.

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Solution

All possible ordered pairs $= (^{3} C_{1}) \times (^{3} C_{1}) = 9$

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Q. Use elements of set P = {2 , 3} to find the number of all possible ordered pairs.

A = {5, 6, 7}

B = {3, 4}

. Form all possible ordered pairs and write the total number of ordered pairs formed so that the first component is from set A and second component is from set B.

What is the total number of such pairs?

Q. (a) What is the minimum number of ordered pairs to form a non-zero reflexive relation on a set of n elements?
(b) On the set R of real numbers S is a relation defined as

S

(x, y) | x ϵ R, y ϵ R, x + y = x y

a ϵ R

such that 'a' is never the first element of an ordered pair in S. Also find

b ϵ R

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(c) Consider the function

f (x) = \frac{3 x + 4}{x - 2}, x \neq 2

. Find a function

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on a suitable domain such that

(g o f) (x) = x = (f o g) (x)

R

be an equivalance relation on a finite set

A

n

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Let R be an equivalence relation on a finite set A having n elements. Then the number of ordered pairs in R is

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