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In this problem, we have to provide a counter example to the following statements.
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Now, a counter example says that we're going to let our first part of the statement be true.
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So we're going to say let our p be true.
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P is true.
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But we need to find where q is not true.
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Q is not true.
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All that means is that we just have to find one instance where this is not true.
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So, for instance, every geometric figure with a right angle, with four right angles, is a square.
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So we'll have a rectangle.
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A rectangle has four right angles, but it is not a square.
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So that is our counter example.
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If a real number is not positive, then it must be negative.
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So we need a number that is not positive, but also not negative.
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Well, that's going to be zero.
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Zero is neither positive nor negative, so that's our counter example.
00:51
Now, for each natural number in, if n is greater than three, then three divides n squared minus one.
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So what we need here is a number that's bigger than three that we can set n squared minus one.
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And that number is not going to be divisible by three.
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So i'm going to say let n be six.
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Let n equal six.
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Then that would have six squared minus one.
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And that's going to equal 36 minus one...