Page 147 - Mathematics_Form_Two

Sets

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11. C {natural numbers less than 20} their elements. The categories include:
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12. D {perfect squares numbers} finite, infinite, singleton, and empty sets.
13. Determine whether each of the Finite set
following is a set and provide a A set is finite if it contains a countable
reason for your answer. number of elements. For instance,
FOR ONLINE READING ONLY
(a) {3, 5, 7, 11} A= {a, b, c, d, e}is a finite set because its
elements can be counted.
(b) {dog, cow, stone, goat}
(c) {a, e, i, o, u} Infinite set
(d) {Asia, Africa, Europe, Australia} A set is infinite if it contains an uncountable
(e) {January, Monday, Wednesday, number of elements. When representing Mathematics for Secondary Schools
November} infinite sets, a few elements are listed
followed by an ellipsis () to indicate
14. List the elements of each of the that the list does not have an end. For
following sets: instance, A = {2, 4, 6, 8, ...} is an infinite

(a) P = {last three consonants of set because the entire elements can not be
English alphabets} counted.
(b) D = {months beginning with Empty set
the letter J} An empty set is a set which has no
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(c) F {prime numbers less than elements. It is also called as a null or void
set. For instance, the set of prime numbers
20} between 31 and 37 is an empty set because
15. Describe the following sets in there is no prime number between 31 and
set builder notation. 37. An empty set is denoted by the symbol
(d) The set of all letters in the word { } or Ø.
“PROBABILITY”. Singleton set
(e) The set of reciprocals of natural A singleton set is a set that contains only
numbers. one element. For instance, H = {2}.
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(f) B {1, 3, 9}
Comparison of sets
16. Describe each of the following sets Two or more sets can be compared and
in roster form. classified as equivalent sets, equal sets or
(a) { :xx∈ and x ≤ 3} one is a subset of the other.

(b) {x : x is the letter in the word Equivalent sets
PROPORTION}
n Two sets are equivalent if they have the

(c) {x : x = and 1≤3,n∈ !} same number of elements. Normally, the
n +1 symbol "" is used to denote equivalent.
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For instance, set A = {2, 4, 6, 8} and set
Types of sets B = {a, b, c, d} are equivalent because
Sets can be categorised into different they have equal number of elements. That
types based on the number and nature of is, (A)n = n (B) = 4.

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Student's Book Form Two

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