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Q9  Let R be the relation on Z defined by R = \left \{ ( a,b) : a , b \epsilon Z , a-b\: \: is \: \: an \: \: integer \right \}
      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 R = \left \{ \right.(x, x^3) : x\: \: is\: \: a\: \: prime\: \: number \: \: less\: \: than\: \: 10\: \: \left. \right \} 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
      R = \left \{ ( x , x +5 ): x \epsilon \left \{ 0,1,2,3,,4,5 \right \} \right \}

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
             \left \{ ( a,b): a ,b \epsilon A , b\: \: is\: \: exactly \: \: divisible\: \: by \: \: a \right \}  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
             \left \{ ( a,b): a ,b \epsilon A , b\: \: is\: \: exactly \: \: divisible\: \: by \: \: a \right \}  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
             \left \{ ( a,b): a ,b \epsilon A , b\: \: is\: \: exactly \: \: divisible\: \: by \: \: a \right \}  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
R = \left \{ ( x,y ) : the \: \: diffrence \: \: between \: \: x \: \: and \: \: y \: \: is \: \: odd ; x \epsilon A , y \epsilon B \right \}. 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 R = \left \{ ( x,y ) : y = x +5 , x is a natural number less than 4 ; x , y \epsilon N \left. \right \}. 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
R = \left \{ ( x,y): 3x -y = 0 , where \: \: x , y \epsilon A \right \} . 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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