Assignment 5

# Assignment 5 - Pranav Soneji Assignment 5 100428383...

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Pranav Soneji Assignment 5 100428383 Discrete Mathematics Assignment #5 7.1 Recurrence Relations (page 457): Exercise 8 8. Find the solution to each of these recurrence relations with the given initial conditions. Use an iterative approach such as that used in Example 5. a) : : b) c) = = : : = = d) : : = =

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Pranav Soneji Assignment 5 100428383 e) : : f) : : g) We have 2 cases When n is odd .... When n is even ....
Pranav Soneji Assignment 5 100428383 Therefore, we have 7.5 Inclusion-Exclusion (page 505): Exercise 20 20. How many elements are in the union of five sets if the sets contain 10,000 elements each, each pair of sets has 1000 common elements, each triple of sets has 100 common elements, every four of the sets have 10 common elements, and there is I element in all five sets? Using the Inclusion-Exclusion Principle:

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Pranav Soneji Assignment 5 100428383 8.5 Equivalence Relations (page 565): Exercise 48 48. List the ordered pairs in the equivalence relations produced by these partitions of {a, b, e, d, e, f, g}. a) {a, b}, {c, d}, {e, f, g} ={(a, a), (a, b), (b, a), (b, b), (c, c), (c, d), (d, c), (d, d), (e, e), (e, f), (e, g), (f, e), (f, f), (f, g), (g, e), (g, f), (g, g)} b) {a}, {b}, {c, d}, {e, f}, {g} =
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