Mathematics for Computer Science

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Chapter 15
Cardinality Rules
Problem 15.2.
In how many different ways is it possible to answer the next chapter’s practice
problems if:
the first problem has four true/false questions,
the second problem requires choosing one of four alternatives, and
the answer to the third problem is an integer 15 and 20?
Problem 15.3.
How many total functions are there from set A to set B if jAj D 3 and jBj D 7?
Problem 15.4.
Let X be the six element set fx 1 ; x 2 ; x 3 ; x 4 ; x 5 ; x 6 g.
(a) How many subsets of X contain x 1 ?
(b) How many subsets of X contain x 2 and x 3 but do not contain x 6 ?
Class Problems
Problem 15.5.
A license plate consists of either:
3 letters followed by 3 digits (standard plate)
5 letters (vanity plate)
2 characters—letters or numbers (big shot plate)
Let L be the set of all possible license plates.
(a) Express L in terms of
A D fA; B; C; : : : ; Zg
D D f0; 1; 2; : : : ; 9g
using unions ([) and set products ().
(b) Compute jLj, the number of different license plates, using the sum and product
rules.