why inverse of a conditional statement seems to be TRUE?
Consider following conditional statment:
If two points are distinct, then there is exactly one line that passes through them.
Inverse is as follows:
If two points are not distinct, then it is not true that there is exactly one line that passes through them.
According to high school geometry book, inverse is always FALSE but in above example inverse seems to be TRUE. If both points are same, then, more than one line can pass through them.
If two points are distinct, then there is exactly one line that passes through them.
Inverse is as follows:
If two points are not distinct, then it is not true that there is exactly one line that passes through them.
According to high school geometry book, inverse is always FALSE but in above example inverse seems to be TRUE. If both points are same, then, more than one line can pass through them.
ASKER CERTIFIED SOLUTION
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
SOLUTION
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
ASKER
> It seems that either high school geometry book is incorrect, or you have misinterpreted what it said.
Here is the link to the book:
http://www.nexuslearning.net/books/ML-Geometry/Chapter2/ML%20Geometry%20Chapter%202%20Review-Test.pdf
Please look at equivalent statements on page 72.
Here is the link to the book:
http://www.nexuslearning.net/books/ML-Geometry/Chapter2/ML%20Geometry%20Chapter%202%20Review-Test.pdf
Please look at equivalent statements on page 72.
SOLUTION
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
ASKER
> if two points are distinct, then they are the same points
I disagree.
I disagree.
pardon, meant "not-distinct"
typo
typo
SOLUTION
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
>>If two points are not distinct, then it is not true that there is exactly one line that passes through them.
if two points ARE distinct, then it is True that there is exactly one line that passes through them.
if two points ARE distinct, then it is True that there is exactly one line that passes through them.
SOLUTION
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
While I see the book giving an example of an inverse that is false, I see nowhere any claim that inverse is always false.
ASKER
Superb job!
Incredible excellent answers in such a short time.
Genuis minds!
Incredible excellent answers in such a short time.
Genuis minds!
if two points are distinct, then they are the same points
point a = 3,3
point b = 3,3
there can be many lines that pass through
so any line going through 3,3 is true.
the inverse would be a mirror line on the opposite quardant, thus it will not pass through