Each of the items on the LEFT (numbered) is a mistaken proof that any integer di

Question

Each of the items on the LEFT (numbered) is a mistaken proof that any integer divisible by 6 is divisible by 3. Match the mistaken proof with the description of the mistake.


Match the numbers with the letter:
1.) Let n be an integer that is divisible by 6. We want to prove that n is divisible by 3. Let n = 3k for some integer 3. Then n is divisible by 3.

2.) Suppose n is any number divisible by 6. Then n = 6n for some integer n, so n = (3) (2)n, and n is divisible by 3.

3.) Suppose n is divisible by 6 and 3. Then n = 6k and n = 3m for integers k and m. Thus n is divisible by 3.

4.) 24 is divisible by 6, and 24 is 3*8. 216 is divisible by 6, and 216 is 3* 72. 0 is divisible by 6 and 0 is 3*0. Thus if n is divisible by 6, n is divisible by 3.



a.) Using the same letter to mean different things.

b.) Jumping to conclusion.

c.) Assuming what was to be proved.

d.) Arguing from examples only.

Explanation / Answer

1 --> c 2 --> a 3 --> b 4 --> d

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