or,

"Mrs. Jones, do you know my mother?"

or,

"This is my daughter Ellen, Mrs. Jones."

These are all good form, whether gentlemen are introduced to ladies,
ladies to ladies, or gentlemen to gentlemen. In introducing a gentleman to
a lady, you may ask Mr. Smith if he has met Mrs. Jones, but you must not
ask Mrs. Jones if she has met Mr. Smith!


=FORMS OF INTRODUCTIONS TO AVOID=

Do not say: "Mr. Jones, shake hands with Mr. Smith," or "Mrs. Jones, I
want to make you acquainted with Mrs. Smith." Never say: "make you
acquainted with" and do not, in introducing one person to another, call
one of them "my friend." You can say "my aunt," or "my sister," or "my
cousin"--but to pick out a particular person as "my friend" is not only
bad style but, unless you have only one friend, bad manners--as it implies
Mrs. Smith is "my friend" and you are a stranger.

You may very properly say to Mr. Smith "I want you to meet Mrs. Jones,"
but this is not a form of introduction, nor is it to be said in Mrs.
Jones' hearing. Upon leading Mr. Smith up to Mrs. Jones, you say "Mrs.
Jones may I present Mr. Smith" or "Mrs. Jones; Mr. Smith." Under no
circumstances whatsoever say "Mr. Smith meet Mrs. Jones," or "Mrs. Jones
meet Mr. Smith." Either wording is equally preposterous.