In Problem 1.10 from the textbook, I ask you to
   “explain answers both logically and arithmetically”.
Here is an example of how you might present a solution to a similar problem.

Note 1: I don't want you to copy the precise words I use below. This is just to show what KIND of information I want in a solution.
Note 2: The words in [.. ..] are included as my explanation to you; you would not include them in your solutions to the problems -- if you know computer programming, think of them as comments in a computer program.
Note 3: See NOTE at the end of the discussion.

1.10. True or False.

(*) 7 is prime and 5 is even.

We know that 5 is not even (optional: because 5 is not a multiple of 2), so the statement   “5 is even”  is F.
       [..Arithmetic part of explanation..]
For an “AND” statement to be T, both parts must be T.
       [..Logical part of explanation..]

Therefore the given statement is false.

ALTERNATIVE

1.10. True or False.

(*) 7 is prime and 5 is even.

We know that 5 is not even (optional: because 5 is not a multiple of 2), so the statement   “5 is even”  is F.
       [..Arithmetic part of explanation..]
For an “AND” statement to be true, both parts must be true.
       [..Logical part of explanation..]

Therefore the statement “7 is prime and 5 is even” is false.

NOTE that the truth or falsity of the statement  “7 is prime”  is irrelevant to the explanation. Therefore it is a waste of paper, it is a waste of ink (or pencil), and it is a waste of time to include reference to it.

Last modified Aug 23, 2007

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