 Hello and welcome to the session. In this session we will discuss a question which says that a part z is the set of integers described the following relation in words. Give its domain and range. And the relation of the set of other pairs 0 5 0 minus 5 3 4 minus 3 4 3 minus 4 minus 3 minus 4 4 3 minus 4 3 4 minus 3 minus 4 minus 3 5 0 minus 5 0. And b that is let a is a set containing elements e q r f and t and b is a set containing elements u v and w which of the following are relations from a to b. First part r 1 is a set containing ordered pairs e u q v and t w. r 2 is a set containing ordered pairs u r v t and w q. r 3 is a set containing ordered pairs p q r s and t u. Now before starting the solution of this question we should know some results. First is if r be a relation from the set a to the set b then r is equal to the set containing ordered pair x y such that x belongs to a and y belongs to p the domain components in a relation. Now these results will work out as a t idea and now we will start with the solution. In the first part we have to write this relation ordered pair 0 5. Now here we can see that 0 square plus 5 square is equal to 0 plus 25 which is equal to 25 ordered pair from this relation and let us take this ordered pair 4 3. Now here we can also see plus 9 which is equal to 25. Now consider one more ordered pair from this relation. Now here consider minus 5 0 for this also minus 5 square plus 0 square is equal to 25 plus 0 which is equal to 25. Similarly for all ordered pairs you can check that the square of the first component plus the square of the second component in all ordered pairs is equal to 20. The given relation f is equal to 2 plus y square is equal to 25 where x square belongs to have to find the domain and range of this relation. Now using these results which are given in the t idea domain is a set of all ordered pairs in this relation. So here these are the first components of all ordered pairs. So domain of the relation r is equal to set containing the elements 0 3 minus 4 5 and minus 5. Second components in the given relation now for this relation r the range of r is equal to set containing the elements 0 minus 3 3 minus 4 4 5 minus 5. Now we will start with the part b in which set a and b are given to us. Now given the elements b q r is the first containing the elements u v and w. Now we have to check that whether this is a relation from a to b or not. Now for the first part is given as the set containing the ordered pairs p u and t w. Now using this result which is given in the key idea from a to b if components in all the ordered pairs and t are from the set a and set are u v and w. So this is yes. This is a relation from a to b in the ordered pair x y such that x belongs to a and y belongs to b. Now let us start with the second part. Now in the second part containing the ordered pairs u r v t and w q. Now for this to be a relation from a to b the first components of all the ordered pairs should be ordered pairs should be from the set b. But u v and w this is no this is not a relation from a to b because the first components. Now let us start with the third part equal to a set containing the ordered pairs t u such b. Now here you can see that in these that is p u r and s are from the set. This is not a relation from a to b because in the ordered pairs p q which is given question and that is all for this session. Hope you all have enjoyed the session.