The following statement is true: “∀ nonzero numbers x, ∃ a real number y such that xy = 1.” For each x given below, find a y to make the predicate “xy = 1” true.
a. x = 2
b. x = −1
c. x = 3/4
The following statement is true
\(\forall\) non-zero numbers \(x, \exists\) a real number \(y\) such that \(x y=1\)
(a) \(x=2\)
There exists a real number \(y=\frac{1}{2}\) such that \(x y=2 \cdot \frac{1}{2}=1\)
(b) \(x=-1\)
There exists a real number \(y=-1\) such that \(x y=(-1)(-1)=1\)
(c) \(x=\frac{3}{4}\)
There exists a real number \(y=\frac{4}{3}\) such that \(x y=\frac{3}{4} \cdot \frac{4}{3}=1\)