A: "There exists an integer greater than 5 such that it is less than 10"
B: "There exists an integer such that it is greater than 5 and less than 10."
C: "There exists an integer less than 10 such that it is greater than 5."
D: "There exists an integer such that it is less than 10 and greater than 5."
I know that A can be translated to B (likewise C to D).
B and D are obviously equivalent, whereas I don't think A and C are.
Thus, I believe that A implies B but not vice-versa (likewise C implies D but not vice-versa). But is this correct??