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(a) Use De Morgan's laws to write
the negation of |
[3] |
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-1 < x < 4 |
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(b) Use truth tables to test the
validity of the following arguments. |
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(i) |
p ® q |
[3] |
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q |
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\ p |
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(ii) |
p ®
q |
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ù q |
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\ ù p |
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(iii) |
p ®
q |
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ù p |
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\ ù q |
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(c) Using your answers from part
(b), are the following arguments valid or not. |
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(i) If x is larger than 2, then its
square is larger than 4. |
[1] |
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x is not larger than 2 |
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\The square of x
is not larger than 4. |
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(ii) If Jane solved this problem correctly,
then Jane obtained the answer 2. |
[1] |
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Jane obtained the answer 2. |
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\Jane solved this
problem correctly. |
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(iii) If this is a dog, then it has four legs. |
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It does not have four legs. |
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\It is not a dog. |
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(d) Prove the following using
Mathematical Induction. |
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What kind of series is this? |
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