स्वच्छता दिवस या पखवाड़े पर प्रतिवेदन लिखें
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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.
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इसमें मुख्य रूप से आसपास के क्षेत्र में समुदाय को कचरा प्रबंधन एवं खुले में शौच नहीं कर घर के शौचालय का उपयोग करने पर जोर दिया जाएगा। छह सितंबर को विद्यालय में हरियाली के लिए अभियान चलाना है। ... 11 सितंबर को विद्यालयों में स्वच्छता ही सेवा दिवस का आयोजन करना है। इसमें विद्यालय स्तर पर स्वच्छता ही सेवा अभियान किया जाना है
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