Guess the B'Day

Logic Level 3

Miss Jas, a teacher whose birthday is M/D (where M is month, D is day) has two students, Joy and Wen. Both students know that Miss Jas' birthday is one of the following:
2/15, 2/20,
4/14, 4/15, 4/18,
6/14, 6/17,
8/2, 8/18, 8/20
Miss Jas told M to Joy and told D to Wen. She then asked the two students the question, "Do you know what my birthday date is?"

Joy says: "If I do not know, Wen does not know it either".
Wen says: "I didn’t know it at first, but now I know".
Joy says: "Oh, then I know it too now".

So what is Miss Jas' birthday date?

Image credit: Wikipedia Twice25.

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