# More Logic

• Sep 12th 2008, 09:48 AM
NeedHelp18
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.
• Sep 12th 2008, 10:04 AM
Plato
"P only if Q."

a) Write it as a conditional statement. $P \to Q$
b) Write it's reciprocal (converse?). $Q \to P$
c) Write its counterpositive. (contrapositive?) $\neg Q \to \neg P
$
• Sep 12th 2008, 10:09 AM
NeedHelp18
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
• Sep 12th 2008, 10:21 AM
Plato
P="A and B are sets, and A is a subset of B" and Q="A U B = B."
• Sep 12th 2008, 10:34 AM
NeedHelp18
Please tell me if my answers are right.

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.
• Sep 12th 2008, 10:40 AM
Plato
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.
• Sep 12th 2008, 10:50 AM
NeedHelp18
Wait, so i have to use if and then for every one? im at a loss
• Sep 12th 2008, 10:54 AM
Plato
Quote:

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.
• Sep 12th 2008, 11:21 AM
NeedHelp18
ohh ok i get it, so other than inserting if, and then, are they correct?
especially the second problem
• Sep 12th 2008, 11:24 AM
Moo
Quote:

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 : $P \Rightarrow Q$ is translated into "If P, then Q" or "Q, if P" or "P, only if Q"
• Sep 12th 2008, 11:27 AM
Plato
Quote:

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.