Question

who short the elephant?​

Answer 1

Answer:

In discrete Maths, a relation is said to be antisymmetric relation for a binary relation R on a set A, if there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other. In a formal way, relation R is antisymmetric, specifically if for all a and b in A, if R(x, y) with x ≠ y, then R(y, x) must not hold, or, equivalently, if R(x, y) and R(y, x), then x = y. Hence, as per it, whenever (x,y) is in relation R, then (y, x) is not. Here x and y are the elements of set A. Apart from antisymmetric, there are different types of relations, such as:

Reflexive

Irreflexive

Symmetric

Asymmetric

Transitive

An example of antisymmetric is: for a relation “is divisible by” which is the relation for ordered pairs in the set of integers. For relation, R, an ordered pair (x,y) can be found where x and y are whole numbers and x is divisible by y. It is not necessary that if a relation is antisymmetric then it holds R(x,x) for any value of x, which is the property of reflexive relation.

Antisymmetric Relation Definition

In set theory, the relation R is said to be antisymmetric on a set A, if xRy and yRx hold when x = y. Or it can be defined as, relation R is antisymmetric if either (x,y)∉R or (y,x)∉R whenever x ≠ y.

A relation R is not antisymmetric if there exist x,y∈A such that (x,y) ∈ R and (y,x) ∈ R but x ≠ y.

Note: If a relation is not symmetric that does not mean it is antisymmetric.

Answer 2

Answer:

In discrete Maths, a relation is said to be antisymmetric relation for a binary relation R on a set A, if there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other. In a formal way, relation R is antisymmetric, specifically if for all a and b in A, if R(x, y) with x ≠ y, then R(y, x) must not hold, or, equivalently, if R(x, y) and R(y, x), then x = y. Hence, as per it, whenever (x,y) is in relation R, then (y, x) is not. Here x and y are the elements of set A. Apart from antisymmetric, there are different types of relations, such as:

Reflexive

Irreflexive

Symmetric

Asymmetric

Transitive

An example of antisymmetric is: for a relation “is divisible by” which is the relation for ordered pairs in the set of integers. For relation, R, an ordered pair (x,y) can be found where x and y are whole numbers and x is divisible by y. It is not necessary that if a relation is antisymmetric then it holds R(x,x) for any value of x, which is the property of reflexive relation.

Antisymmetric Relation Definition

In set theory, the relation R is said to be antisymmetric on a set A, if xRy and yRx hold when x = y. Or it can be defined as, relation R is antisymmetric if either (x,y)∉R or (y,x)∉R whenever x ≠ y.

A relation R is not antisymmetric if there exist x,y∈A such that (x,y) ∈ R and (y,x) ∈ R but x ≠ y.

Note: If a relation is not symmetric that does not mean it is antisymmetric.