For sets A and B, define the relation E to be AEB A B = Is E relation symmetric or transitive ? Justify Solution not reflexive: A intersected with A is not the empty set yes symmetric: A intersected with B is the same as B intersected with A not transitive: if b is the empty set the A^B=empty set and B^C=empty set but A^C can be nonempty.

1. For sets A and B, define the relation E to be AEB A B = Is E relation symmetric or transitive ?
Justify
Solution
not reflexive: A intersected with A is not the empty set yes symmetric: A
intersected with B is the same as B intersected with A not transitive: if b is the empty set the
A^B=empty set and B^C=empty set but A^C can be nonempty