Working with recursions.

The sequence of catalan numbers, for each integer n > or equal to 1. Show that the sequence satisfies the recurrence relation Csubk= 4k-2/k+1 for all integers k>or equal to 2.

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Discrete - Let A = {1, 2, 3, 4, 5, 6,12} and define the relation R on A by m R n iff m|n. Write the definitions of the properties, reflexive, antisymmetric and transitive and the use of the definitions to determine whether each property holds for this relation. See attached file.

Working with permutations and combinations - Permutations and coefficients (a) How many bit strings of length 7 are there? Explain. (b) How many bit strings of length 7 are there which begin with a 0 and end with a 1? Explain. (c) How many bit strings of length 7 is there that contain an even number of ones? Explain.

Using combinations to determine the all possible number of ways. - An award presentation has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia and Paul. In how many ways can the awards alternate between men and women with the first award being presented to a woman?

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