Answer to Question #303303 in Discrete Mathematics for Joyce

Question

If A = {1, 2, 3} and B = {4, 5, 6}, state which of the following is a relation from A to B.

(a) R₁ = {(1, 4); (2, 5); (6, 3)}

(b) R₂ = {(2, 5); (3, 6)}

(c) R₃ = {(6, 3); (5, 2); (4, 1)}

(d) R₄ = {(1, 5); (1, 6); (2, 4); (2, 6), (3, 4), (3, 5)}

Answer 1

Solution:

A = {1, 2, 3} and B = {4, 5, 6}

A relation from A to B will include elements from A×B

Elements of A×B are

{(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)}

R₁ contains (6,3) which is not the element of A×B. So, not a relation.

R₃ contains (6,3) which is not the element of A×B. So, not a relation.

Thus, R₂ and R₄ are relations from A to B.

So, options b and d are correct.