The phrase "a rejecting" is not correct and usable in written English.
It is not a standard construction and lacks clarity without additional context.
Example: "The committee issued a rejecting statement regarding the proposal."
Alternatives: "a refusal" or "a denial".
Instead of a rejecting bullying, he now espouses "muscular liberalism".
Dancers on knees or reclining suggested lovers, or even a love triangle, with a rejecting turn of the head.
Her daughter has had to mourn her father and recover from a rejecting stepfather — and here comes her now sober, but still judgmental and narcissistic, grandmother.
After all, Tony Soprano (a "sociopath," a "criminal, not a sociopath," a "psychologically complex psychopath" or a man with "a vertical split," depending on whom you ask) was raised by a rejecting mother and a mobster father.
A slightly more complex automaton accepts Qeven: again there are two states, a start state = the accepting state and a rejecting state, and this time remain in the same state when 0's are scanned, but go to the other state when a 1 is scanned.
It is easy to construct a finite automaton accepting ∀ (or ∀rel = all), i.e., checking that w consists only of 1's: just remain in the start state = accepting state as long as 1's are encountered, but go to a rejecting state as soon as a 0 is scanned, and remain there whatever is encountered afterwards.
