a) x=z
b) x<z
c) x is rational then for some y, xy is irrational.
d) x is an even integer then for some integer xy is odd.
Apparently this question is hard
Let be a property which involves a and b. Let be a property which involves c. For this problem, the domain will be the reals. For each of the following below, find properties and such that:
a.) is true.
b.) is false.
c.) is true.
d.) is false.
Why y? Why not z?
Oh I see I guess it doesn't matter. So, my answer can be:
a) x=z
b) x<z
c.) If , then
d.) If , then
Right? Although not sure how c and d are both not in the rationals (that is irrational), since one is true and the other is false, and we know that rational + rational = rational and similarly for rational*rational.
c is true, but isn't false?