WEBVTT

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Hi, I'm Fiona.

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Let's have a look at TMUA 2021,
paper 2 and question 10.

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We're told that the first 7 terms of a
sequence of positive integers are the

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following,
and we're asked to consider the following

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statement about the sequence.

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So statement star says that if N is a
prime number,

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then UN is a multiple of three or UN is a
multiple of 5.

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And we're asked what is the smallest
value of north that provides A

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counterexample to this statement star.

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And then we're given all the possible
options to choose from 1:00 to 7:00.

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So let's have a look at each of the terms
of this sequence for which N is prime,

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and then we're going to look at whether
that term is a multiple of three or a

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multiple of five.

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OK,
so the first prime number we come to is 2.

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We can see that this term 21 is a
multiple of 3,

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so that's not going to provide a
counterexample.

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Next prime number we come to is three or
the third term,

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and we can see that this term is a
multiple of 3 and it's a multiple of 5.

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So that doesn't provide a counter example.

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It's important here to consider that in
mathematical logic when we say or,

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that is an inclusive or.

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So it can mean that both things are true
or that one of them is true,

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and it's important to keep that in mind
with these kind of questions.

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Next prime number we come to is the term
U5 and that is 44.

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And we can see that 44 is not a multiple
of three.

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It's also not a multiple of 5.

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And so the smallest value of N that
provides a count, for example, is n = 5.

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And then I'm going to look over and I can
see that E is the answer.

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So option E is the answer to this
question.

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Let's take a moment to reflect on this
question.

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And firstly,
I just want to think about these terms

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here.

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So the terms for which N is not prime.

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So that would be U1U4U6.

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We don't even need to consider those
because this statement doesn't apply to

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them at all because this statement is
only looking at N when N is prime.

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So what we need to do is to look at the
the the terms of the sequence for which N

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is prime and then consider one of those
that does not satisfy being a multiple of

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three or a multiple of 5.

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Next thing I want to point out is that
it's interesting to me that they chose

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for the first term to be a multiple of
three and a multiple of five.

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I was thinking that they might try and
catch some of us out by making us want to

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think that one is a prime number.

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But of course, 1 is not a prime number.

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And it's important to have that in mind
when we're looking at questions like this.

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And the final thing I want to reflect on
is just to be very confident that we

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understand our terminology.

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So this word or in mathematical logic,
as I said earlier, is an inclusive or.

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And so if we are considering whether one
thing or another thing are satisfied,

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we can have that one or both are
satisfied.

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And that satisfies the definition of the
mathematical term or.