**How to Discuss the Relation For Reflexive Symmetric or Transitive :**

Here we are going to see how to discuss the relation for reflexive symmetric or transitive.

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.

**Question 1 :**

Discuss the following relations for reflexivity, symmetricity and transitivity:

(i) The relation R defined on the set of all positive integers by “mRn if m divides n”.

**Solution :**

**Condition for reflexive :**

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

Every element is divided by itself, for all m ∈ R, m divides m and for all n ∈ R n divides n.

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.

From the given question, we come to know that m divides n, but the vice versa is not true.

For example, if m = 2 and n = 4 ∈ R, then we may say that 2 divides 4. But we cannot say that 4 divides 2. Hence symmetric is not true.

**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.

If m divides n, then n = mk ----(1)

If n divide p, then p = nq ----(2)

Here "k" and "q" are constants.

By applying the value of "n" in (2), we get

p = m k q

From this, we come to know that p is the multiple of m. So, it is transitive.

Hence the given relation is reflexive, not symmetric and transitive.

After having gone through the stuff given above, we hope that the students would have understood, "How to Discuss the Relation For Reflexive Symmetric or Transitive"

Apart from the stuff given in "How to Discuss the Relation For Reflexive Symmetric or Transitive", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**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**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**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 **

**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 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**