Exercises
I. Translate each of the following English phrases into a mathematical
expression. (2points each)
1. the sum of x and the sum of y and z
2. the product of x and the sum of y and z
3. the product of the sum of x and y and the difference of x and y
4. x more than y
II. Translate each of the following mathematical expressions into an
English phrase using the words sum, difference, product and/or
quotient. (2points each)
5. xy + xz
6. z (x −y)
7. ( x + z) + (y −z)
III. Given:
U = {x│x is a counting number from 1 to 15}
X = {x│x is an even number ≤ 12 & divisible by 4}
Y = The set of odd numbers less than 9
W = The set of counting numbers not more than 6
Find: a.) X ꓵ Y b.) (Y ꓵ W) ꓴ X c.) (W ꓴ X)' ꓵ X'
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Exercises
IV. Exercises on of listing method and set-builder
notation.
SET-BUILDER NOTATION
LISTING METHOD
1. 𝒏 ∈ ℕ 𝒏 𝒊𝒔 𝒑𝒓𝒊𝒎𝒆
2. 𝒏𝟐 𝒏 ∈ ℤ
3. 𝒙 ∈ ℝ 𝒙𝟐 − 𝟐 = 𝟎
5.
6.
−𝟔, −𝟒, −𝟐, 𝟎, 𝟐, 𝟒, 𝟔
7.
−𝟏, 𝟎, 𝟏
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Exercises
V. In a class of 50 students, it was found that 21 are
taking up English, 14 are taking up Mathematics, 28
are taking up History, 7 are taking up Math and
English, 10 are taking up Math and History, 11 are
taking up History and English, while 3 are taking up
the three courses. Use the Venn diagram to
determine how many students are taking up the
following subject/s?
1. Mathematics only
2. History and English but not Mathematics
3. English or Mathematics but not History
4. History only
5. Mathematics and English
6. Not taking up any of the three courses
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Exercises
VI. A survey of 1250 Internet users shows the following results
concerning the use of the search engines Google, Bing, Yahoo!, and Ask.
585 use Google.
620 use Yahoo!.
560 use Ask.
450 use Bing.
100 use only Google, Yahoo!, and Ask.
41 use only Google, Yahoo!, and Bing.
50 use only Google, Ask, and Bing.
80 use only Yahoo!, Ask, and Bing.
55 use only Google and Yahoo!.
34 use only Google and Ask.
45 use only Google and Bing.
50 use only Yahoo! and Ask.
30 use only Yahoo! and Bing.
45 use only Ask and Bing.
60 use all four.
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Sets
Use the Venn diagram to determine how many of the Internet users
1. use only Google?
2. use exactly three of the four search engines?
3. do not use any of the four search engines?
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