 Hello and welcome to the session. In this session we will discuss a question which says that that relation r is equal to the set containing the odd appear xx plus 3 such that x is the odd natural number less than 15 x plus r and r inverse prove that domain of r inverse is equal to the range of r. Now before starting the solution of this question we should know our result and that is for the inverse of the relation is given by r inverse where r inverse is equal to the set containing the odd appear yx belongs to r that is if we have to find out the inverse of the relation r then we will be odd appear in the relation r the relations are obtained the inverse of the relation. Now this result will work out as a key idea for solving out this question and now we will start with the solution. Now in the relation it is given that x now lets add natural numbers less than 15 13 which is given that r is the relation that is r is equal to set containing the odd appear natural number less than to the set containing the odd appear. Now the first odd appear will be obtained by putting x is equal to 1 so putting x is equal to 1 here it will be 1 and the second component will be 1 first odd appear will be obtained by putting x is equal to 3 here so it will be 3 and second component will be 3 plus 3. Now the next odd appear will be 7 so it will be 7, 7 plus 3, 9, 9 plus 3 the next odd appear 11 plus 3 and the last will be 13, 13 plus 3 containing the odd appear 1 the next 3, 6 the next will be the next is 9, 12 the next 11, 14, 13. Now using this result which is given in the key idea can be obtained by introducing the first and the second components in these odd appears that is second components in the odd appears of the relation. Therefore r inverse over odd appears 6, 3 will be equal to first components in these odd appears so this is equal to the set containing the elements 14 and now the range of components of these odd appear so it is a set containing the elements. Now this is therefore domain is equal to range of r. Now in the project domain of r inverse is equal to range of r for the given question and that's all for this session hope you all have enjoyed the session.