Compare two character vectors in R

I have two character vectors of IDs.

I would like to compare the two character vectors, in particular I am interested in the following figures:

• How many IDs are both in A and B
• How many IDs are in A but not in B
• How many IDs are in B but not in A

I would also love to draw a Venn diagram.

Here are some basics to try out:

> A = c("Dog", "Cat", "Mouse")
> B = c("Tiger","Lion","Cat")
> A %in% B
[1] FALSE  TRUE FALSE
> intersect(A,B)
[1] "Cat"
> setdiff(A,B)
[1] "Dog"   "Mouse"
> setdiff(B,A)
[1] "Tiger" "Lion" 

Similarly, you could get counts simply as:

> length(intersect(A,B))
[1] 1
> length(setdiff(A,B))
[1] 2
> length(setdiff(B,A))
[1] 2