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Discrete Mathematics An Open Introduction, 4th Edition

Oscar Levin

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1.
Consider the eight bit strings of length 3. Let’s find the number of strings that start with 1 or have weight 2 (i.e., contain exactly two 1s).
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(a)
List all the 3-bit strings that start with 1.
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Answer.
\(\text{111}, \text{110}, \text{101}, \text{100}\)
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(b)
List all the 3-bit strings that have weight 2.
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Answer.
\(\text{110}, \text{101}, \text{011}\)
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(c)
Now list all the 3-bit strings that start with 1 or have weight 2. But be lazy: Don’t list them from scratch. Use your lists from the two tasks above.
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Answer.
\(\text{111}, \text{110}, \text{101}, \text{100}, \text{011}\)
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2.
How did you combine your two lists above? Explain how you did it. Then think of another method you could have used, and explain how that would be different.
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3.
Xiang and Omari are discussing their favorite mathematicians throughout history. Xiang has a list of 7 favorites, while Omari has a list of 5. They discover that they have 3 mathematicians in common. How many mathematicians are on their combined list?
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Answer.
\(9\)
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