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As i understand, there is a mistake in condition, and P(x,y) denote the sentence , otherwise it is independent from y, which doesn't make much sence.
a. ⱯxⱯyP(x,y). For x = 0 and y = 1 we have , which is false
This statement is false
b. ⱯxƎyP(x,y). Let , then , which means we can find such y, for exmaple, , that P(x, y) is true
This statement is true
c. ƎxⱯyP(x,y). Let , then , but we can put, for example,
, which means P(x, y) would be false
So, this statemnet is false
d. ƎxƎyP(x,y). For x = 0 and y = 0 we have . P(x, y) is true
This statement is true. Also this statement implies from the true statement (b)