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Online Quiz (Worksheet A B C D)

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High School Mathematics
8.8 Types of Relations - Reflexive, Symmetric, Anti-Symmetric, Transitive, and Equivalance

1. Reflexive Relation:
R is a relation in A and for every a A, (a,a) R then R is said to be a reflexive relation.

Example:
Every real number is equal to itself. Therefor "is equal to " is a reflexive relation in the set of real numbers.

2. Symmetric Relation:
R is a relation in A and (a,b) R implies (b,c) R then R is said to be a symmetric relation.

Example:
In the set of all real numbers "is equal to" relation is symmetric.

3. Anti-Symmetric Relation:
R is a relation in A. If (a,b) R and (b,a) R implies a = b, then R is said to be an anti-symmetric relation.

Example:
In set of all natural numbers the relation R defined by "x divides y if and only if (x,y) R" is anti-symmetric. For x|y and y|x then x = y.

4. Transitive Relation:
R is a relation in A if (a,b) R and (b,c) R implies (a,c) R is called a transitive relation.

Example:
In the set of all real numbers the relation "is equal to" is a transitive relation. For a = b, b = c implies a = c.

5. Equivalence Relation:
A relation R in a set A is said to be an equivalence relation if it is reflexive, symmetric and transitive.

Example:
In the set of all real numbers the relation "is equal to" is an equivalence relation for a R, a = a, b = a implies b = a and a = b, b = c implies a = c.


Directions: Choose the correct answer. Also write at least 10 examples of your own.
Q 1: The relation "is subset of" is not an equivalence relation since it is ______.
not symmetric
symmetric

Q 2: "is congruent to" relation in the set of coplanar triangle is _____ relation
All are correct
Reflexive
Transitive
Symmetric

Q 3: Every reflexive relation in a set A is an _____.
An Equivalence relation
Anti-symmetric relation
Transitive relation
not an Anti-symmetric relation

Q 4: R is a relation in A. If (a,b) R and (b,c) R implies (a,c) R, then R is called a _______.
Reflexive relation
Anti-symmetric relation
Transitive relation
Symmetric relation

Question 5: This question is available to subscribers only!

Question 6: This question is available to subscribers only!


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