I can't figure out how to interpret this. Is my understanding of the statement correct?
"There exists an x such that for all y, if p(x) is true then x = y"
i. P(0) = true, if y = 1 then x != y, formula is not true. p(1) = true, if y = 0 then, x != y, this formula is not true.
ii. P(0) = true, same as above. P(1) = false, since the premise is false the statement should be true. But of course x != y if y = 0
Same for iii.
Am I sort of making sense?