x is a positive odd integer --> x + 2 is a positive odd integer
The trouble comes in negating each statement when finding the contrapositive
do i negate the statements to:
x is a NEGATIVE odd integer
x + 2 is a NEGATIVE odd integer
x is a positive EVEN integer
x + 2 is a positive EVEN integer
x is a NEGATIVE EVEN integer
x + 2 is a NEGATIVE EVEN integer
or (likely not but i just thought i'd ask) U = universe
x is a positive odd U-Z
x + 2 is a positive odd U-Z
I know that a statement has a truth value, but my prof and the text never went over what parts of a statement are eligible for negation. Is it right to say that the statements I have used as examples are in fact statements even though x is unknown, because they are quantified?
Am I correct to say that the quantification of these statements is implicit rather than explicit?
Argh this seems like a lot of questions, I'd really appreciate it someone could answer at least a few of them if answering them all is too laborious.