Question

there are two statement to be explained ​

Answer 1

QuestioN :

Q1. Void relation ( null relation ) is always symmetricity as well transitive.

Q2. Singleton Relation is always transitive.

AnsWer :

• Void ( null ) : define as For A relation to be symmetricity If whenever aRb then, bRa
• A relation on set A to symmetricity if Whenever ( a , b ) ∉ R then, ( b , a ) ∉ R.

Transitive Relations :

• A relation on a set A to transitive, if Whenever ( a , b ) ∈ R and ( b , c ) ∈ R then, ( a , c ) ∈ R
• A relation on a set A to transitive, if Whenever ( a , b ) ∈ R and ( b , c ) ∉ R then, ( a , c ) ∉ R
• A relation on a set A to transitive, if Whenever ( a , b ) ∉ R and ( b , c ) ∈ R then, ( a , c ) ∉ R.
• A relation on a set A to transitive, if Whenever ( a , b ) ∉ R and ( b , c ) ∉ R then, ( a , c ) ∉ R.

So, Void relation ( null relation ) is always symmetricity as well transitive.

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2. Transitive Relations : Relation define as A relations on set A is set to be transitive, if Whenever order pair ( a , b ) ∈ R and order pair ( b , c ) ∈ R then, order pair ( a , c ) ∈ R.

SomE MorE condition be change.

• A relations on set A is set to be transitive, if Whenever order pair ( a , b ) ∈ R and order pair ( b , c ) ∉ R then, order pair ( a , c ) ∉ R.
• A relations on set A is set to be transitive, if Whenever order pair ( a , b ) ∉ R and order pair ( b , c ) ∈ R then, order pair ( a , c ) ∉ R.

Example :

• R is Relation in S = { 2 , 3 , 4 , 5 }

R = { ( 2 , 3 ) , ( 3 , 4 ) , ( 4 , 5 ) }

• Here you notice R is not transitive relations.

So, Singleton relation is not always transitive.