Introduction of binary relations:-
In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = A × A. More generally, a binary relation between two sets A and B is a subset of A × B. The terms dyadic relation and 2-place relation are synonyms for binary relations.(Source: Wikipedia).
I like to share this Octal to Binary Converter with you all through my article.
Example problems for binary relation:-
Problem 1:-
Find four binary relations from `{a,b}` to `{x,y}` that are not functions from `{a,b}` to `{x,y}`
Solution:-
R = `{(a, x), (a, y), (b, x)} ` is not a function from `{a, b}` to `{x, y}` because two values related to a
R = `{(a, x)} ` is not a function from `{a, b}` to `{x, y}` because there are no values related to b
It able to find another two easily. In fact, of the 16 binary relations from `{a, b}` to `{x, y}` , only 4 are functions, and 12 are not functions.
Problem 2:-
Find four binary relations from `{a,b,c}` to `{x,y,z}` that are not functions from `{a,b,c}` to `{x,y,z}`
Solution:-
R = `{(a,x),(a,y),(a,z),(b,x),(b,y),(b,z),(c,x),(c,y),(c,z)} ` is not a function from` {a,b,c}` to `{x,y,z}` because three values related to a.
R = `{(a, x)}` is not a function from `{a, b, c}` to `{x, y,z}` because there are no values related to b & c.
It able to find another two easily. In fact, of the 36 binary relations from `{a, b, c}` to `{x, y, z}` , only 6 are functions, and 30 are not functions. Please express your views of this topic What is Rational Number by commenting on blog.
More example problems for binary relation:-
Problem 1:-
Do you understand the following calculations?
X = `{1,2,3}`
|x| = 3.
Solution:-
X x X = `{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)}`
| X x X | = 9
|P(X x X)| = `2^9`
Because a binary relation on X is any subset of pairs in X x X there are `2^9` possible binary relations on X.
(Some authors say` 2^9 -1` because of not liking an empty relation.)
Problem 2:-
Do you understand the following calculations?
X = `{1,2,3,4}`
|x| = 4.
Solution:-
X x X = `{(1,1),(1,2),(1,3),(1,4)(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}`
| X x X | = 16
|P(X x X)| = `2^16`
Because a binary relation on X is any subset of pairs in X x X there are` 2^16` possible binary relations on X.
(Some authors say `2^16 -1` because of not liking an empty relation.)
In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = A × A. More generally, a binary relation between two sets A and B is a subset of A × B. The terms dyadic relation and 2-place relation are synonyms for binary relations.(Source: Wikipedia).
I like to share this Octal to Binary Converter with you all through my article.
Example problems for binary relation:-
Problem 1:-
Find four binary relations from `{a,b}` to `{x,y}` that are not functions from `{a,b}` to `{x,y}`
Solution:-
R = `{(a, x), (a, y), (b, x)} ` is not a function from `{a, b}` to `{x, y}` because two values related to a
R = `{(a, x)} ` is not a function from `{a, b}` to `{x, y}` because there are no values related to b
It able to find another two easily. In fact, of the 16 binary relations from `{a, b}` to `{x, y}` , only 4 are functions, and 12 are not functions.
Problem 2:-
Find four binary relations from `{a,b,c}` to `{x,y,z}` that are not functions from `{a,b,c}` to `{x,y,z}`
Solution:-
R = `{(a,x),(a,y),(a,z),(b,x),(b,y),(b,z),(c,x),(c,y),(c,z)} ` is not a function from` {a,b,c}` to `{x,y,z}` because three values related to a.
R = `{(a, x)}` is not a function from `{a, b, c}` to `{x, y,z}` because there are no values related to b & c.
It able to find another two easily. In fact, of the 36 binary relations from `{a, b, c}` to `{x, y, z}` , only 6 are functions, and 30 are not functions. Please express your views of this topic What is Rational Number by commenting on blog.
More example problems for binary relation:-
Problem 1:-
Do you understand the following calculations?
X = `{1,2,3}`
|x| = 3.
Solution:-
X x X = `{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)}`
| X x X | = 9
|P(X x X)| = `2^9`
Because a binary relation on X is any subset of pairs in X x X there are `2^9` possible binary relations on X.
(Some authors say` 2^9 -1` because of not liking an empty relation.)
Problem 2:-
Do you understand the following calculations?
X = `{1,2,3,4}`
|x| = 4.
Solution:-
X x X = `{(1,1),(1,2),(1,3),(1,4)(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}`
| X x X | = 16
|P(X x X)| = `2^16`
Because a binary relation on X is any subset of pairs in X x X there are` 2^16` possible binary relations on X.
(Some authors say `2^16 -1` because of not liking an empty relation.)
No comments:
Post a Comment