Which statement about E. coli RNA polymerase (core enzyme) is FALSE?

A) In the absence of the $\sigma$ subunit, core polymerase has little specificity for where initiation begins.
B) The core enzyme contains several different subunits.
C) The core enzyme has no polymerizing activity until the $\sigma$ subunit is bound.
D) The RNA chain grows in a 5' $\rightarrow$ 3' direction.
E) The RNA product is complementary to the DNA template.