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WHY in sign language
How to sign "why" in American Sign Language (ASL)? And, "why not".
Meaning: For what reason or purpose.
Pronunciation (sign description): In the "Y" handshape with palm facing the side of upper head side, three fingers (index finger, middle finger, and ring finger) of dominant hand flap down twice.
Contextual variation (sign description): In the "8-thumb-open" handshape with palm facing the side of upper head side, the middle finger of dominant hand flaps down few times.
There are nuances of meaning with the movements of the hand as well as repetitions of the movement used by Deaf signers.
Grammar: Use furrowed eyebrows for a question in sentence.
Related WH-question signs
The job of a detective is to figure out the WHY, or as we call it in the biz, the motive. It's the first component to solving a crime/. If you can figure out why, then it's just a matter of time before everything else falls into place. Well, first you have to have a WHAT. The what is usually a crime. WHERE is typically a bank or fancy vault of some sort. HOW usually involves an intricate heist… that or guns. You can tell WHICH by WHEN it happens. If it's at night, it's a heist. If it's during the day, it's probably a robbery. You're also going to have to take into consideration HOW MUCH they took. Once you piece all that together, you're left with one burning question. WHO? This we may never know, because they were wearing a mask, and they got away. If only we had a clue.
But, why? BECAUSE I say so. But why? Why not!
Meaning: "Why not" used to make a suggestion or to express agreement.
Written ASL
[Note: ASL writing is not an official standard. This sign language writing remains in a state of open space to allow room for experiment, evolution, and improvement.]

Written ASL digit for "why" contributed by Adrean Clark the ASLwrite community, 2017.