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Question 261270: Determine the truth value of the following statement:
Leonhard Euler was a famous mathematician and the sum of any two odd numbers is an even number.
Is this true or false?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
In order for a statement consisting of two statements joined by "and" to be a true statement, both of the constituent statements must be true. Let us first examine the second of your two constituent statements. The  -th odd number is  . The  -th odd number is  . The sum of these two odd numbers is then:
\ +\ \left(2m\,-\,1\right)\ =\ 2n\,+\,2m\,-\,2)
The sum is clearly divisible by 2 and is therefore an even number, hence the second part of the compound statement is true.
So, it all comes down to your definition of "famous mathematician." If you believe that Herr Euler was a mathematician and that he was famous, whatever that means, then the first part of the compound statement is true. It is very possible that the statement posed is true for some people and false for others. For example, I would unhesitatingly say that the statement is true, because I believe Leonhard Euler to be not only "a" famous mathematician, but "the" famous mathematician. Other people, deplorably ignorant in my view, have never heard of him and therefore must deny the statement.
John
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