Check whether values in one data frame column exist in a second data frame

Use %in% as follows

A$C %in% B$C

Which will tell you which values of column C of A are in B.

What is returned is a logical vector. In the specific case of your example, you get:

A$C %in% B$C
# [1]  TRUE FALSE  TRUE  TRUE

Which you can use as an index to the rows of A or as an index to A$C to get the actual values:

# as a row index
A[A$C %in% B$C,  ]  # note the comma to indicate we are indexing rows

# as an index to A$C
A$C[A$C %in% B$C]
[1] 1 3 4  # returns all values of A$C that are in B$C

We can negate it too:

A$C[!A$C %in% B$C]
[1] 2   # returns all values of A$C that are NOT in B$C

  2 %in% B$C   # "is the value 2 in B$C ?"  
  # FALSE

  A$C[2] %in% B$C  # "is the 2nd element of A$C in B$C ?"  
  # FALSE