Question

A = {1 , 2, 3} , B = {2 , 4 , 6 }

R = { (1,2) , (1,4) , (3, 2) , (3,4)}

a) Show that R is a relation from A to B

b) Write domain , co–domain and range of R
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Answer 1

Answer:

Solution:

Since, R = {(3, 6); (4, 7); (5, 8)} then Domain (R) = {3, 4, 5} = A

We observe that no two ordered pairs in R have the same first component.

Therefore, R is a mapping from A to B.

(ii) Let A = {1, 2, 3} and B= {7, 11} and R = {(1, 7); (1, 11); (2, 11); (3, 11)}

Solution:

Since, R = {(1, 7); (1, 11); (2, 11); (3, 11)} then Domain (R) = {1, 2, 3} = A

But the ordered pairs (1, 7) (1, 11) have the same first component.

Therefore, R is not a mapping from A to B.

Answer 2

Answer:

a) if we see the elements of R of the form(a,b)

a=1,3 and b=2,4

so a€A and b€B

THUS R is a relation from A toB

B) domain- 1,3

range -2,4

co-domain -- 2,4,6