Final Review Information

The Final exam will be on Tuesday (5/7) from 8 to 9:50 AM in Wright 5. It will be closed book and notes, except you will be allowed to bring your purple sheet of Logic Rules and three other sheet of paper (8.5" x 11" both sides) with notes. (Like your cheat sheet for test 1, test 2, and the Final)

The final will emphasize the material since the last test, but some questions will be over the material from Tests 1 and 2.

Below are the hightlights of the textbook sections since the last exam:

Section 3.1

Topics: Definitions of sets, set operations (union, intersection, complement, cross product), power set.

Standard sets: etc.

Skills:

Describe a set by listing elements and by a characteristic property.

Prove that one set is a subset of another

Find the power set of a set

Check that the required properties for a binary and unary operation are satisfied.

Prove set identities by showing set inclusion in each direction or using the basis set identities.

Section 3.2

Topics: Decision Trees, Multiplication Principle, Addition Principle, combining the Multiplication and Addition Principles

Skills:

Be able to count the number of outcomes

Section 3.3

Topics: Principle of Inclusion and Exclusion, Pigeonhole Principle

Skills:

Be able to find the number of elements in the union of sets using the Principle of Inclusion and Exclusion.

Be able to find the minimum number of elements in a set to guarantee two elements with the same property.

Section 3.4

Topics: Permutation, Factorial, Combination

Skills:

Find the number of permutations of r distinct objects chosen from n distinct objects.

Find the number of combinations of r distinct objects chosen from n distinct objects.

Use permutations and combinations in conjunction with the Multiplication Addition Principles.

Find the number of permutations of n objects that are not all distinct.

Find the number of permutations of r objects out of n distinct objects when objects may be repeated.

Find the number of combinations of r objects out of n distinct objects when objects may be repeated.

Section 3.5

Topics: Difficulty of calculating the number of combinations due to the large factorials and the finite size of integer representation on the computer. Using Pascal's triangle to calculate the number of combinations.

Section 4.1

Definition of a binary relation. Operations on binary relations on a set include union, intersection, and complementation. Properties of binary relations (reflexivity, symmetry, transitivity, and antisymmetry).

Skills:

Be able to test an ordered pair for membership in a binary relation.

Be able to test a binary relation for reflexivity, symmetry, transitivity, and antisymmetry.

Draw the Hasse diagram for a partially ordered set.

Section 4.4 only the subsection on Order of Magnitude of Functions (pp.295 - 300)

Topics: Definition of Order of Magnitude (theta notation, ). Definition of Big-Oh

(O( )) notation.

Skills:

Be able to apply the definitions of Order of Magnitude (theta notation, ) and Big-Oh

(O( )) notation to find the constant c's and n₀ given a execution time function.

For a given section of code containing nested loops, be able to

• provide a reasonable Big-Oh notation (upper-bound estimate on the execution time)
• trace the code to determine how many times the inner-most loop executes
• determine the Order of Magnitude/Theta notation ("exact" estimate on the execution time)