Exercises on Section 2

Exercise 4

Let A be the set of integers between 100 and 999 inclusive.

• (a) Express A in the form A = {x ∈ ?? : condition}
  
• (b) What is the cardinality of A?
  

Answer

Solution

• (a) A = {x ∈ Int : 100 ≤ x and x ≤ 999}. (There are other correct solutions.)
  
• (b) There are 999 integers between 1 and 999 inclusive. The set A does not contain the integers between 1 and 99 inclusive, and there are 99 of these. So A has cardinality 999 − 99 = 900.
  

Exercise 5

If B = {s ∈ SeqOfChar : s starts with ‘T’ and s has length 4}, which of the following is a member of the set B?

• (a) “This”.
  
• (b) [‘T’, ‘h’, ‘i’, ‘s’, ‘.’].
  
• (c) [“T”, “h”, “i”, “s”].
  
  

Answer

Solution

• (a) “This” is in B. It is a string (a sequence of characters), it contains four characters (so has length 4), and it starts with the character ‘T’.
  
• (b) [‘T’, ‘h’, ‘i’, ‘s’, ‘.’] is not in B. It is a string starting with ‘T’, but it contains five characters (has length 5). (Do not forget to count the character ‘.’.)
  
• (c) [“T”, “h”, “i”, “s”] is not in B. Each member of this sequence is a string, not a character. (Note that “T”, etc, are enclosed in double inverted commas.)
  

Exercise 6

Suppose that each possible time of the day is stored as a pair of integers, where the first integer gives the hour and the second integer gives the minute. For example, (14, 45) represents a quarter to three in the afternoon. (Midnight is (0, 0) rather than (24, 00).) Express the set of possible times of the day in the form {(h, m) ∈ ?? : condition}).

Answer

Solution

The set is {(h, m) ∈ Int × Int : 0 ≤ h and h < 24 and 0 ≤ m and m < 60}.