What would George Washington do?
When you’re introducing two individuals (man or woman) to each other always introduce the younger to the older. So if Jim is in his 20’s and Joe is in his 50’s you say “Joe I’d like to introduce you to JIm”. If introducing a man and a woman of around the same age always introduce the man to the woman. For example, “Jane I’d like to introduce you to Jim”.
G-dub