MATH 122
CHUKA UNIVERSITY
UNIVERSITY EXAMINATIONS
EXAMINATION FOR THE AWARD OF DEGREE OF DEGREE OF BACHELOR
OF EDUCATION (ARTS,SCIENCE) ,BACHELOR OF SCIENCE, BACHELOR OF
ARTS (MATHS-ECON), BACHELOR OF SCIENCE (COMP SCI,APPLEIED COMP
SCI),BACHELOR OF SCIENCE (ECON STATS)
MATH 122: BASIC MATHEMATICS
STREAMS: TIME: 2 HOURS
DAY/DATE: WEDNESDAY 13/12/2017 11.30 A.M – 1.30 P.M
INSTRUCTIONS:
Answer Question ONE and ANY Other TWO Questions.
Do not write on the question paper.
QUESTION ONE (30 MARKS)
a. Using venn diagrams show that (i) A – (B ∪ C) = (A-B) ∀ ∩ (A –C) [2marks]
(ii) (A-B) ∩ (A ∩B) = ∅ (2 marks)
b. (i) Let r denote `` It is raining’’ and s denote `` it is snowing ‘’. Write the English
sentences corresponding to the following ;
i. 𝑟 ~𝑠 (1 mark)
ii. ~𝑟 → 𝑠 (1 mark)
iii. ~𝑟 ↔ ~(𝑠 𝑟) (1 mark)
c. Construct the truth table for the following proposition to determine whether is a
fallacy, tautology or an in derterminate.
𝑝 → 𝑞 ↔ ~𝑞 → (~𝑝 ∧ ~𝑞) (3marks)
d. Let 𝑋 = 1, 2, 3, 4 𝑎𝑛𝑑 𝑌 = 1, 2, 3 . Define a relation R by the set
𝑹= 𝑥, 𝑦 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑥 ≤ 𝑦 ∀𝑥 ∈ 𝑋, 𝑦 ∈ 𝑌 . Find the set R. (3marks)
e. How many ways are there to select a first prize winner, a second prize winner and a
third prize winner from 50 different people who have entered a contest? (3 marks)
Page 1 of 3
CHUKA UNIVERSITY
UNIVERSITY EXAMINATIONS
EXAMINATION FOR THE AWARD OF DEGREE OF DEGREE OF BACHELOR
OF EDUCATION (ARTS,SCIENCE) ,BACHELOR OF SCIENCE, BACHELOR OF
ARTS (MATHS-ECON), BACHELOR OF SCIENCE (COMP SCI,APPLEIED COMP
SCI),BACHELOR OF SCIENCE (ECON STATS)
MATH 122: BASIC MATHEMATICS
STREAMS: TIME: 2 HOURS
DAY/DATE: WEDNESDAY 13/12/2017 11.30 A.M – 1.30 P.M
INSTRUCTIONS:
Answer Question ONE and ANY Other TWO Questions.
Do not write on the question paper.
QUESTION ONE (30 MARKS)
a. Using venn diagrams show that (i) A – (B ∪ C) = (A-B) ∀ ∩ (A –C) [2marks]
(ii) (A-B) ∩ (A ∩B) = ∅ (2 marks)
b. (i) Let r denote `` It is raining’’ and s denote `` it is snowing ‘’. Write the English
sentences corresponding to the following ;
i. 𝑟 ~𝑠 (1 mark)
ii. ~𝑟 → 𝑠 (1 mark)
iii. ~𝑟 ↔ ~(𝑠 𝑟) (1 mark)
c. Construct the truth table for the following proposition to determine whether is a
fallacy, tautology or an in derterminate.
𝑝 → 𝑞 ↔ ~𝑞 → (~𝑝 ∧ ~𝑞) (3marks)
d. Let 𝑋 = 1, 2, 3, 4 𝑎𝑛𝑑 𝑌 = 1, 2, 3 . Define a relation R by the set
𝑹= 𝑥, 𝑦 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑥 ≤ 𝑦 ∀𝑥 ∈ 𝑋, 𝑦 ∈ 𝑌 . Find the set R. (3marks)
e. How many ways are there to select a first prize winner, a second prize winner and a
third prize winner from 50 different people who have entered a contest? (3 marks)
Page 1 of 3
