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Q9  Let R be the relation on Z defined by
Find the domain and range of R.

It is given that Now, as we know that the difference between any two integers is always an integer. And  As Domain of R = set of all first elements of the order pairs in the relation. Therefore,  The domain of R = Z Now, Range of R = set of all second elements of the order pairs in the relation. Therefore,  range of R = Z Therefore, the domain and range of R is Z and Z  respectively

Q8  Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.

It is given that  A = {x, y, z} and B = {1, 2} Now, Therefore, Then, the number of subsets of the set Therefore, the number of relations from A to B is

Q7  Write the relation in roster form.

It is given that   Now, As we know the prime number less than 10 are 2, 3, 5 and 7. Therefore,  the relation in roaster form is ,

Q6  Determine the domain and range of the relation R defined by

It is given that    Therefore, the relation in roaster form is ,  Now, As Domain of R = set of all first elements of the order pairs in the relation. Therefore,  Domain of   Now, As Range of R = set of all second elements of the order pairs in the relation. Range of     Therefore,  the domain and range of the relation R is    respectively

Q5 (3)   Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by
Find the range of R.

It is given that   A = {1, 2, 3, 4, 6} And  Now, As the range of R = set of all second elements of the order pairs in the relation. Therefore,  Range of

Q5 (2)   Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by
Find the domain of R

It is given that   A = {1, 2, 3, 4, 6} And  Now, As Domain of R = set of all first elements of the order pairs in the relation. Therefore,  Domain of

Q5 (1)   Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by
Write R in roster form

It is given that   A = {1, 2, 3, 4, 6} And  Therefore, the relation in roaster form is ,

Q4 (2)   The Fig2.7 shows a relationship between the sets P and Q. Write this relation  roster form. What is it  domain  and range? From the given figure. we observe that  P = {5,6,7}, Q = {3,4,5}  And the relation in roaster form is ,   As Domain of R = set of all first elements of the order pairs in the relation. Therefore,  Domain of   Now, Range of R = set of all second elements of the order pairs in the relation. Therefore, the range of

Q4 (1)  The Fig2.7 shows a relationship between the sets P and Q. Write this relation
in set-builder form It is given in the figure that  P = {5,6,7}, Q = {3,4,5}  Therefore,  the relation in set builder form is ,    OR

Q3   A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by
. Write R in
roster form.

It is given that   A = {1, 2, 3, 5} and B = {4, 6, 9} And  Now, it is given that the difference should be odd. Let us take all possible differences. (1 - 4) = - 3, (1 - 6) = - 5, (1 - 9) = - 8(2 - 4) = - 2, (2 - 6) = - 4, (2 - 9) = - 7(3 - 4) = - 1, (3 - 6) = - 3, (3 - 9) = - 6(5 - 4) = 1, (5 - 6) = - 1, (5 - 9) = - 4 Taking the difference which are odd we get, Therefore, the relation in...

Q2  Define a relation R on the set N of natural numbers by is a natural number less than . Depict this relationship using roster form. Write down the domain and the range.

It is given that is a natural number less than As x is a natural number which is less than 4. Therefore, the relation in roaster form is,   As Domain of R = set of all first elements of the order pairs in the relation. Therefore,  Domain of    Now, Range of R = set of all second elements of the order pairs in the relation. Therefore,  the range of    Therefore,  domain and the...

Q1  Let A = {1, 2, 3,...,14}. Define a relation R from A to A by
. Write down its domain, codomain and
range.

It is given that  Now, the relation R from A to A is given as Therefore, the relation in roaster form is ,   Now, We know that  Domain of R = set of all first elements of the order pairs in the relation Therefore, Domain of    And Codomain of R = the whole set A i.e.   Codomain of    Now, Range of R = set of all second elements of the order pairs in the...
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