Midterm Examination Review MATH 210G Fall, 2012 Instructions ...

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6. a) Starting with the first 4 rows of Pascal’s triangle, compute the next seven rows. 1 1 1 1 2 1 1 3 3 1 b) How many distinct subsets are there of a set having ten elements In general, how many distinct subsets are there of a set having N elements Hint: consider the cases N = 0, 1, 2, 3 and look for a pattern. The set containing no elements is called the empty set. The empty set is a subset of every set. In particular, the empty set has one subset and a set with one element has two distinct subsets: the empty set and the element itself. c) Ten kids want to play a game of basketball. How many distinct ways are there to divide the kids into two teams each with five players d) How many distinct ways are there to divide the kids into two teams each with at least one player, and all other players on the other team
7. • Translate each sentence into an implication of the form A → B or˜B →Ã, then determine the intended implication of the following statements: Good poker players cannot be trusted People who wear fancy shoes are not lucky in love. Everyone is good in poker except nerds. You can trust people who wear shabby shoes. • Translate each sentence into an implication of the form A → B or˜B →Ã, then determine the intended implication of the following statements: No shark ever doubts that he is well fitted out. A fish, that cannot dance a minuet, is contemptible. No fish is quite certain that it is well fitted out, unless it has three rows of teeth. All fishes, except sharks, are kind to children. No heavy fish can dance a minuet. A fish with three rows of teeth is not to be despised. • Translate each sentence into an implication of the form A → B or˜B →Ã, then determine the intended implication of the following statements: No kitten that loves fish is unteachable. No kitten without a tail will play with a gorilla. Kittens with whiskers always love fish. No teachable kitten has green eyes. No kittens have tails unless they have whiskers. • Translate each sentence into an implication of the form A → B or˜B →Ã, then determine the intended implication of the following statements: Animals that do not kick are always unexcitable. Donkeys have no horns. A buffalo can always toss one over a gate. No animals that kick are easy to swallow. No hornless animal can toss one over a gate. All animals are excitable, except buffalo. • Translate each sentence into an implication of the form A → B or˜B →Ã, then determine the intended implication of the following statements: All who neither dance on tightropes nor eat penny-buns, are old. Pigs that are liable to giddiness are treated with respect. A wise balloonist takes an umbrella with him. No one ought to lunch in public, who looks ridiculous and eats penny-buns.
Page 1 and 2: Midterm Examination Review MATH 210
Page 3 and 4: 3. The 36 possible outcomes of roll
Page 5: 5. • Two new students are assigne
Page 9 and 10: 8. • Fill in the values T or F fo

Midterm Examination Review MATH 210G Fall, 2012 Instructions ...

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