I have an example: If A > B, then A is a red color.
and If B > A, then B is a red color.
I would like to change it to s shorter way like :
If A>B, then A is a red color, and vice versa.
or If A>B, then A is a red color, the other way around.
Which one is correct and incorrect? have you got any other ways to explain it?
Thank a lots!
Neither of your statements says what you want.
There are potential misunderstandings with the use of 'vice versa'. Your example illustrates this well.
Logically*, 'vice versa' means conversely
. The "vice versa" of:
"If A>B, then A is a red color"
"If A is a red colour, then A>B", (the converse)
not:"If A>B, then A is not a red color"
(the inverse) or:
"If B>=A, then A is a red colour. " (A is red regardless of whether A>B or B>A or B=A.)
There's nothing in your statement that makes B a red color.
Actually, you've missed the case of A=B.
You might mean:
If A>B, then A is a red color
Else if A=B then (something)
Else B is a red color.
You'll note that these are not logically the same.The "vice versa" is not a logical implication - that's why it needs to be stated if it is true."A hates B" does not imply that "B hates A". The latter is the converse, or "vice versa" of the former.
The "vice versa"of:
"John brought Meg to the dance, and Michael brought Alice
" could be: "Meg brought John to the dance, and Alice brought Michael.
"Michael brought Alice to the dance and John brought Meg."
In fact, I'd say the vice versa is not defined for that example, as it is
for a simpler proposition, "A hates B".
Barb's 2nd and 3rd examples have easily identified converses, so 'vice versa' is not ambiguous, and it's easily understood - which is not the case in your propositions.
- statement: if p then q
- converse: if q then p
- inverse: if not p then not q
- contrapositive: if not q then not p