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Question 762783: Would you pls help me to answer this:
3. Arianna is trying to determine if the following statement is always, sometimes, or never true:
The square of a prime number is odd.
She writes the following statements: 32 = 9, 52 = 25, 72 = 49, 112 = 121, and 132 = 169.
Based on her results, she concludes that the relation function statement is always true.
a.What kind of reasoning did Arriana use?
b.Is her conclusion correct? If not, use a counterexample to prove why it is not.
c.Use deductive reasoning to determine whether the following statement is always or never true.
The sum of an odd number and an even number is odd
Thanks
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! a.What kind of reasoning did Arriana use?
She used inductive reasoning (since she's listing examples and trying to determine an overall pattern or rule from them)
b.Is her conclusion correct? If not, use a counterexample to prove why it is not.
Her conclusion is not correct because 2 is a prime number but 2^2 = 4 is NOT odd. So the overall statement is false.
c.Use deductive reasoning to determine whether the following statement is always or never true.
The sum of an odd number and an even number is odd
Let n and m be any integers
2n is even, so 2n+1 is odd
2m is even
Odd + Even = 2n+1 + 2m = 2n+2m + 1 = 2*(n+m) + 1 = 2*q + 1
where q is an integer
which proves that Odd + Even = Odd
Therefore the statement "The sum of an odd number and an even number is odd" is always true
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