Eliminate Any Ambiguity
Inclusive OR vs Exclusive OR
If k is a positive integer,
then either k is even
or k2 is positive.
If k is an integer,
then either k is even
or k + 1 is even, but not both.
The Order of Quantifiers Matters
For every positive real number x,
there exists a real number y
such that xy = 1.
There exists a real number y
such that
xy = 1
for every positive real number x.