Thread: Discrete Math

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.

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.

Originally Posted by Plato

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.

Two questions:

where does y come from, and for c do you mean "if x is rational, then for some z, xz is rational" ?

Originally Posted by DiscreteW

Two questions:

where does y come from, and for c do you mean "if x is rational, then for some z, xz is rational" ?

NO!
P(x)="x is rational"
Q(x,y)="xy is not rational"
These predicates work for both (c)

For (d) Q(x,y)="x+y is not rational"

Originally Posted by Plato

NO!
P(x)="x is rational"
Q(x,y)="xy is not rational"
These predicates work for both (c)

For (d) Q(x,y)="x+y is not rational"

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?