1. ## More Logic

"A whole number x is odd only if x^2 is an odd whole number."

a) Write it as a conditional statement.
b) Write it's reciprocal.
c) Write its counterpositive.

" If A and B are sets, and A is a subset of B, then A U B = B."

a) Write its reciprocal.
b) Write its counterpositive.

2. "P only if Q."

a) Write it as a conditional statement. $\displaystyle P \to Q$
b) Write it's reciprocal (converse?). $\displaystyle Q \to P$
c) Write its counterpositive. (contrapositive?) $\displaystyle \neg Q \to \neg P$

3. ok i think i figured it out for the first one, but in the second problem, which is p and which is q? im confused, thanks

4. P="A and B are sets, and A is a subset of B" and Q="A U B = B."

More Logic
"A whole number x is odd only if x^2 is an odd whole number."

a) Write it as a conditional statement. x is odd only if x^2 is odd.
b) Write it's reciprocal. x^2 is odd if x is odd.
c) Write its counterpositive. x^2 is not odd if x is not odd.

" If A and B are sets, and A is a subset of B, then A U B = B."

a) Write its reciprocal. A U B = B only if A and B are sets, and A is a subset of B.
b) Write its counterpositive. A U B is not equal to B if A and B are not sets, and A is not a subset of B.

6. Sorry. But none of those is correct.
Here is the first one.
If A whole number x is odd then x^2 is an odd whole number.

7. Wait, so i have to use if and then for every one? im at a loss

8. Originally Posted by NeedHelp18
Wait, so i have to use if and then for every one? im at a loss
Yes, that is the whole point.

9. ohh ok i get it, so other than inserting if, and then, are they correct?
especially the second problem

10. Originally Posted by NeedHelp18
Wait, so i have to use if and then for every one? im at a loss
What you have to keep in mind is that it's not the order of the way you write it that makes the logic, but the prepositions, namely if (and then)

Think of it : $\displaystyle P \Rightarrow Q$ is translated into "If P, then Q" or "Q, if P" or "P, only if Q"

11. Originally Posted by NeedHelp18
ohh ok i get it, so other than inserting if, and then, are they correct?
especially the second problem
Yes, if you "move" the ifs/thens correctly.