Latching memory ??

I need an output to turn and stay high after the start button has gone back to false.
A latch from a momentary start
So input button goes high output goes high when input button goes back to false output remains high

You are supposed to detect transition on the button, say from low to high, and set output to high when you see this transition. To do this, store the button state and compair with new button state.

heaintdead:
So input button goes high output goes high when input button goes back to false output remains high

so when the input goes high you put the output in high and not touch it again. the output would only go low if you set it low, so unless there is more to the story, this seems pretty straight forward.

CheapB:
so unless there is more to the story,

That's what I suspect. Let's wait and see what the OP will respond.