Testbook Relations in discrete maths

Question

Which of the following statement is not true?

• 1

  If a relation on a set A is symmetric and transitive then R is reflexive.

• 2

  If a relation R on a set A is irreflexive and transitive then R is antisymmetric.

• 3

  If R is antisymmetric relation then R ꓵ S and R U S is antisymmetric for any relation S on A.

• 4

  If R and S are transitive relation on a set A then R U S need not be transitive and R ꓵ S are also transitive.

Comments

for option A) R={   } then in this case  here relation is symmentric transitive but not reflexive

option B)R={(2,4),(4,6),(2,6)} not any set is possible which is transitive  irrefelexive and Antisymmetric

optionC)Intersection part is correct but union  can be create pair with violation of antisymmetric

optionD) this is statement is right similarly as option C

correct ANS is A and C