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ioda
3 years ago
8

What is a counterexample for the conjecture? Any number that is divisible by four is also divisible by eight

Mathematics
1 answer:
Cloud [144]3 years ago
3 0
The value 12 is a good counterexample. It is divisible by 4 (since 12/4 = 3 is a whole number with no remainders or decimal portions) but 12 is not divisible by 8 (note how 12/8 = 1 remainder 4 = 1.5)

To find other examples, add 8 to 12 to get 20. Then add on 8 more to get 28. This pattern continues on forever. 
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Who Washes? Erica and Aaron, who are siblings, have decided to use a lottery system to decide who will wash dishes every night.
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Given that Erica and AAron,are using lottery system to decide who will wash dishes every night.

They put some red and blue power chips and draw each one.  If same colour, Aaron will wash and if not same colours Erica will wash

If the game is to be fair, then both should have equal chances of opportunity for washing.

i.e. Probability for Erica washing = Prob of Aaron washing

i.e. P(different chips) = P(same colour chips)

Say there are m red colours and n blue colours.

Both are drawing at the same time.

Hence Prob (getting same colour) = (mC2+nC2)/(m+n)C2

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The two would be equal is mC2 +nC2 = m+n

This is possible if mC2 =m and nC2 = n.

Or m = 2+1 =3 and n =3

That for a fair game we must have both colours to be 3.


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