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Hi,
I'm Fiona and this is Tamua 2021 paper 2

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and question four.

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We are considering a claim about the
integers AB and C and the claim is that

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if a is a factor of b * C,
then A is a factor of B or A is a factor

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of C.

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And we are asked which of the following
out of 1-2 and three provides A

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counterexample to this claim.

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Now a counterexample is a specific
example which disproves a claim or a

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statement.

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So let's go through each one of these
examples in turn and look for whether

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they disprove this particular claim.

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For the first example,
B is 10 and C is 20.

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That means that BC is 200.

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Now here A is 55 is a factor of 200 that
should say and five is a factor of B as

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well, which is 10,
and 5 is a factor of C which is 20.

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And so this is not a counterexample
because A is a factor of both.

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Now, at this stage,
I'll just mention that it's important to

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be aware of what we mean mathematically
when we use the word or.

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Now in mathematical logic,
or is an inclusive or,

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which means that one or both things can
be true for the OR to hold.

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So if you've ever seen when people say
and Oregon,

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then that really is equivalent to what we
mean by OR in mathematical logic,

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which is inclusive.

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So statement 1 is not a counterexample,
or example 1 is not a counterexample.

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For the second example,
B * C is going to be 4 * 4, which is 16.

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8 is a factor of 16,
but it's not a factor of 4,

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and so this does provide a counterexample
which disproves this claim.

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Here the third example we have,
B * C is 7 * 12, which is going to be 84,

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and A is 6.

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Now 6 is a factor of 84,
which is that first line of our claim,

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and six is not a factor of 7,
but it is a factor of 12.

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So this example 3 is not a counterexample.

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So within these three examples,
we can see that it's only example 2 that

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provides A counterexample to this claim
that we are considering.

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And so scanning my options I can see that
option C says 2 only and that is my

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answer to this question Option C.