Introduction to relations and functions math:
When comparing (relate) the objects (human beings) the concept of relation becomes very important. In a similar fashion we connect two sets (set of objects) by means of relation. A function math is a one of the type of relation. In a function, number two ordered pairs can have the same first element and a different second element. That is, for functions, corresponding to every 1st element of the ordered pairs, there must be a different 2nd element. The relations and functions math example problems and practice problems are given below.
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Example problems for relations and functions math:
Example problem 1:
A function f from N`->` N is defined by f(x) = 7x. Find the range of function
Solution:
The range of f: N ? N is the set of all images of f(x) = 7x, for x = 1, 2, 3, ? N.
The range of f = {7, 14, 21, 28, …}.
Example problem 2:
Let A = {1, 2}, B = {a, b}. Find some relations from A ? B and B ? A.
Solution:
Since relation from A to B is a subset of the Cartesian product
A × B = {(1 , a) , (1, b) , (2 , a) , (2 , b)} any subset of A × B is a relation from A ? B.
{(1 , a), (1 , b), (2 , a), (2 , b)}, {(1, a), (1, b)}, {(1, b, (2, b)}, {(1 , a)} are some relations from A to B.
Similarly any subset of B × A = {(a , 1), (a , 2), (b , 1), (b , 2)} is a relation from B to A.
{(a , 1), (a , 2), (b , 1), (b , 2)}, {(a, 1), (b, 1)}, {(a, 2), (b, 1)} are some relations from B to A.
Example problem 3:
A relation R is defined on the set {–2, 0, 1, 2, 3, 5} as R = {(–2,1), (3,0), (2,5)}. Write down the domain and the range of R.
Solution:
Domain of R is the set of all 1st elements of the ordered pairs in R
Domain = {–2, 3, 2}
Range of R is the set of all 2nd elements of the ordered pairs in R.
Range = {1, 0, 5}.
I have recently faced lot of problem while learning properties of prime numbers, But thank to online resources of math which helped me to learn myself easily on net.
Practice problems for relations and functions math:
Practice problem 1:
In the set N of natural numbers, define the relation R by x Ry if x + y = 9. Find n(R).
Answer: R = {(1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1)} and n(R) = 8.
Practice problem 2:
Let I be the set of integers. R on I is defined as a R b if a – b is an even integer. Prove that R is an equivalence relation.
When comparing (relate) the objects (human beings) the concept of relation becomes very important. In a similar fashion we connect two sets (set of objects) by means of relation. A function math is a one of the type of relation. In a function, number two ordered pairs can have the same first element and a different second element. That is, for functions, corresponding to every 1st element of the ordered pairs, there must be a different 2nd element. The relations and functions math example problems and practice problems are given below.
Please express your views of this topic Exponential and Logarithmic Functions by commenting on blog.
Example problems for relations and functions math:
Example problem 1:
A function f from N`->` N is defined by f(x) = 7x. Find the range of function
Solution:
The range of f: N ? N is the set of all images of f(x) = 7x, for x = 1, 2, 3, ? N.
The range of f = {7, 14, 21, 28, …}.
Example problem 2:
Let A = {1, 2}, B = {a, b}. Find some relations from A ? B and B ? A.
Solution:
Since relation from A to B is a subset of the Cartesian product
A × B = {(1 , a) , (1, b) , (2 , a) , (2 , b)} any subset of A × B is a relation from A ? B.
{(1 , a), (1 , b), (2 , a), (2 , b)}, {(1, a), (1, b)}, {(1, b, (2, b)}, {(1 , a)} are some relations from A to B.
Similarly any subset of B × A = {(a , 1), (a , 2), (b , 1), (b , 2)} is a relation from B to A.
{(a , 1), (a , 2), (b , 1), (b , 2)}, {(a, 1), (b, 1)}, {(a, 2), (b, 1)} are some relations from B to A.
Example problem 3:
A relation R is defined on the set {–2, 0, 1, 2, 3, 5} as R = {(–2,1), (3,0), (2,5)}. Write down the domain and the range of R.
Solution:
Domain of R is the set of all 1st elements of the ordered pairs in R
Domain = {–2, 3, 2}
Range of R is the set of all 2nd elements of the ordered pairs in R.
Range = {1, 0, 5}.
I have recently faced lot of problem while learning properties of prime numbers, But thank to online resources of math which helped me to learn myself easily on net.
Practice problems for relations and functions math:
Practice problem 1:
In the set N of natural numbers, define the relation R by x Ry if x + y = 9. Find n(R).
Answer: R = {(1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2), (8,1)} and n(R) = 8.
Practice problem 2:
Let I be the set of integers. R on I is defined as a R b if a – b is an even integer. Prove that R is an equivalence relation.
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