Let R1 and R2 be symmetric relations.
Let us prove that R1∩R2 is also symmetric relation. Let (a,b)∈R1∩R2. Then (a,b)∈R1 and (a,b)∈R2. Since R1 and R2 are symmetric relations, we conclude that (b,a)∈R1 and (b,a)∈R2. It follows that (b,a)∈R1∩R2, and hence R1∩R2 is also symmetric.
Let us prove that R1∪R2 is also symmetric relation. Let (a,b)∈R1∪R2. Then (a,b)∈R1 or (a,b)∈R2. Since R1 and R2 are symmetric relations, we conclude that (b,a)∈R1 or (b,a)∈R2. It follows that (b,a)∈R1∪R2, and hence R1∪R2 is also symmetric.
Comments
Leave a comment