IF THE GIVEN RELATION IS REFLEXIVE SYMMETRIC OR TRANSITIVE

If the Given Relation is Reflexive Symmetric or Transitive :

Here we are going to see how to check if the given relation is reflexive, symmetric and transitive.

Reflexive, Symmetric and transitive Relation

Let S be any non-empty set. Let R be a relation on S. Then

• R is said to be reflexive if a is related to a for all a ∈ S.
• R is said to be symmetric if a is related to b implies that b is related to a.
• R is said to be transitive if “a is related to b and b is related to c” implies that a is related to c.

If the Given Relation is Reflexive Symmetric or Transitive - Practice Questions

Question 1 :

Discuss the following relations for reflexivity, symmetricity and transitivity:

(iv) Let A be the set consisting of all the female members of a family. The relation R defined by “aRb if a is not a sister of b”.

Solution :

Let A be the relation consisting of 4 female members, a grand mother (a), her two children (b and c) and a grand daughter (d).

Condition for reflexive :

R is said to be reflexive, if a is related to a for a ∈ S.

a is not a sister of a itself. Hence it is reflexive.

Condition for symmetric :

R is said to be symmetric, if a is related to b implies that b is related to a.

aRb that is, a is not a sister of b.

bRa that is, b is not a sister of c.

Note : We should not take b and c, because they are sisters, they are not in the relation.

Hence it is symmetric.

Condition for transitive :

R is said to be transitive if “a is related to b and b is related to c” implies that a is related to c.

aRc that is, a is not a sister of c.

cRb that is, c is not a sister of b.  But a is not a sister of b. Hence it is transitive.

Hence the given relation A is reflexive, symmetric and transitive.

(v) On the set of natural numbers the relation R defined by “xRy if x + 2y = 1”.

Solution :

Condition for reflexive :

R is said to be reflexive, if a is related to a for a ∈ S.

let x = y

x + 2x = 1

3x  =  1  ==>  x = 1/3

1/3 is not related to 1/3, because 1/3 is not a natural number and it is not in the relation.R is not symmetric.

The given set R is an empty relation. An empty relation can be considered as symmetric and transitive.

Hence R is not reflexive, symmetric and transitive.

Related Topics

Reflexive relation

Transitive relation

Equivalence relation

Identity relation

Inverse relation

Difference between reflexive and identity relation After having gone through the stuff given above, we hope that the students would have understood, how to check whether the a relation is reflexive, symmetric or transitive"

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 