For my answer I said that both statements are false for all integers and all real numbers, but I'm not sure if that's correct. Here is my reasoning:
A) There is no x that can multiply by any number y (except zero) to get one. The only number that can multiply by any number and only have one answer is zero, and that answer is zero, not one.
B) There is no z that equals the sum of any x and and any y divded by two because you could plug in any number and get different results ie x=1 y=2, x=3 y=4.
On
It is above question that y=1/x doesn't give an integer even if x is an integer. However, the division is an inner operation for R, and therefore 1/x is a real number for x is real and nonzero. I wasn't able to figure out why you do not consider this situation. For the case of b), I completely agree and prefer not to repeat the same idea here. Let me also formulate how I understand the expression for expression a) for real numbers:
There is x that, for any value y, satisfies the condition y=1/x, which means we plug any value into y and x will be also real (inner operation that doesn't change the space) such that its value is found from1/y
Well that's true but this negates the statement "any value for y". To have a true statement that means for each and every y we try the relationship and we get it correct. Since we have at least one false situation then the statement is not. Let me put it in logical terms: Statement truth value is true= it's (TRUE for y=1) AND (TRUE for y=2) AND (TRUE for y=3)..... Therefore, if any of these terms is not true the truth value is false.