1. The sum of two odd integers is even.2. The sum of two even integers is even.3. The square of an even number is even.4. The product of two odd integers is odd.5. Ifn3+ 5 is odd thennis even, for anyn∈Z.6. If 3n+ 2 is even thennis even, for anyn∈Z.7. The sum of a rational number and an irrational number is irrational.8. The product of two irrational numbers is irrational.9. Use mathematical induction to prove that the firstneven integers add up ton(n+ 1)10. Use mathematical induction to prove thatn3+ 2nis divisible by 3.

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1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Ascientist wants to use a model to present the results of his detailed scientific investigation. why would a model be useful? a )because the model makes the concepts easier to understand b) because the model is easy to put together and to use c) because the model prevents other scientists from asking questions d) because the model requires the audience to pay full attention to it i don't know what to choose because between a and d a is much more likely than d because it only wants to get the attention of the audience. i'm confuse.