Answer to Question #216255 in Discrete Mathematics for Ree

Question

Question 3
Let G and L be relations on A = {1, 2, 3, 4} with G = {(1, 2), (2, 3), (4, 3)} and L = {(2, 2), (1, 3), (3, 4)}.
Which one of the following alternatives represents the relation L ￮ G = G; L?
1. {(2, 3), (3, 3)}
2. {(1, 2), (2, 4), (4, 4)}
3. {(1, 2), (2, 1), (3, 3), (4, 4)}
4. {(2, 4), (4, 4)}

Answer 1

Question 3

Let $G$ and $L$ be relations on $A = \{1, 2, 3, 4\}$ with $G = \{(1, 2), (2, 3), (4, 3)\}$ and $L = \{(2, 2), (1, 3), (3, 4)\}.$

It follows that $L\circ G=\{(2,3),(3,3)\}$ and $G\circ L=\{(1,2),(2,4),(4,4)\}.$ Also note that $L\circ G\ne G$ and $L\circ G\ne L.$