**Finding Inverse of a Relation From the Given Relation :**

Here we are going to see some example problems to understand finding inverse of a relation.

Let A and B be two sets and R be a relation of a set to a set B. Then the inverse of R denoted by R^{-1} is a relation from B to A and is defined by R^{-1 } = {(b, a) : (a, b) ∈ R}

Clearly (a, b) ∈ R <=> R^{-1}

Also, (i) Domain of R = Range(R^{-1}) and

(ii) range (R) = Domain(R^{-1})

**Question 1 :**

Let A be the set of first ten natural numbers and let R be a relation defined by (x, y) ∈ R <=> x + 2y = 10 where R = {(x,y), x ∈ A, y ∈ A and x + 2y = 10. Express R and R^{-1} as the set of ordered pairs. Also determine

(i) Domain of R and R^{-1}

(ii) Range of R and R^{-1}

**Solution :**

To find the set of ordered pairs in the relation, let us apply the values of x one by one in the given function.

x + 2y = 10

y = (10 - x)/2

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

If x = 1 y = 9/2 ∉ A |
If x = 2 y = 8/2 y = 4 |
If x = 3 y = 7/2 ∉ A |
If x = 4 y = 6/2 y = 3 |

If x = 6 y = 4/2 y = 2 |
If x = 8 y = 2/2 y = 1 |
If x = 10 y = 0/2 y = 0 |

R = {(2, 4) (4, 3) (6, 2) (8, 1) (10, 0)}

Domain of R = {2, 4, 6, 8, 10}

Range of R = {4, 3, 2, 1, 0}

R^{-1} = {(4, 2) (3, 4) (2, 6) (1, 8) (0, 10)}

Domain of R^{-1} = {4, 3, 2, 1, 0}

Range of R^{-1} = {2, 4, 6, 8, 10}

**Question 2 :**

A relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows (x, y) ∈ R => x divides y. Express R as the set of ordered pairs and determine the domain and range of R also find R^{-1}.

**Solution :**

R = {(2, 6) (2, 10) (3, 3) (3, 6) (5, 10)}

Domain of R = {2, 3, 5}

Range of R = {3, 6, 10}

R^{-1} = {(6, 2) (10, 2) (3, 3) (6, 3) (10, 5)}

**Question 3 :**

Let R be relation in N defined by (x, y) ∈ R <=> x + 2y = 8. Express R and R^{-1 }as a set of ordered pairs.

**Solution :**

x = 0, 1, 2, ...........

y = (8 - x)/2

If x = 1 y = 7/2 ∉ N |
If x = 2 y = 6/2 y = 3 ∈ N |
If x = 4 y = 4/2 y = 2 ∈ N |

If x = 6 y = 2/2 y = 1 ∈ N |
If x = 8 y = 0/2 y = 0 ∉ N |

R = {(2, 3) (4, 2) (6, 1)}

R^{-1} = {(3, 2) (2, 4) (1, 6)}

After having gone through the stuff given above, we hope that the students would have understood "Finding Inverse of a Relation From the Given Relation".

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

HTML Comment Box is loading comments...

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**

**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**

**Trigonometry 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**