Let A = -1, 0, 1, 2, 3) B = {1, 2, 3, 4, 5) be two sets. R be a relation defined from A to B by R= {(x, y):x+y= 3, x = A, y = B}(i) Write R in the Roster form. (ii) Write the domain and range of R.
Answers
Given:
A = { -1, 0, 1, 2, 3 }
B = { 1, 2, 3, 4, 5 }
To find :
R= {(x, y):x+y= 3, x = A, y = B}
R in the Roster form.
The domain and range of R.
Solution:
Step 1 of 3:
The relation R defined from A to B is given as
R= {(x, y):x+y= 3, x = A, y = B}
R= {(x, y):y = 3 - x, x = A, y = B}
R is defined as, y = 3 - x
when x = - 1
y = 3- ( - 1)
y = 4
when x = 0
y = 3 - 0
y = 3
when x = 1
y = 3 - 1
y = 2
when x = 2
y = 3 - 2
y = 1
when x = 3
y = 3 -3
y = 0
R in roster form,
R = { ( - 1 , 4 ) , ( 0 , 3 ) , ( 1, 2 ) , ( 2 , 1) , ( 3, 0 )
Step 2 of 3:
The domain of R is the set of all first elements of the ordered pairs.
D = { - 1 , 0 , 1 , 2 , 3 }
Step 3 of 3:
The Range of R is defined as the elements used by the function from the set of all second elements of the ordered pairs.
R = { 1 , 2 , 3 , 4 }
Final answer:
R in roster form,
R = { ( - 1 , 4 ) , ( 0 , 3 ) , ( 1, 2 ) , ( 2 , 1) , ( 3, 0 )
Domain of R ,
D = { - 1 , 0 , 1 , 2 , 3 }
Range of R ,
R = { 1 , 2 , 3 , 4 }