Q1. Suppose there are 110 children at a school. Suppose that among these 110 children, 51 children have blue eyes, 33 children have blond hair, and 14 children have blue eyes and blond hair. How many children have neither blue eyes nor blond hair? A. 40 B. 26 C. 84 D. 70 E. 96 F. 12
Q1. Suppose there are 110 children at a school. Suppose that among these 110 children, 51 children have blue eyes, 33 children have blond hair, and 14 children have blue eyes and blond hair. How many children have neither blue eyes nor blond hair? A. 40 B. 26 C. 84 D. 70 E. 96 F. 12
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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Transcribed Image Text:Q1. Suppose there are 110 children at a school. Suppose that among these 110 children,
51 children have blue eyes, 33 children have blond hair, and 14 children have blue
eyes and blond hair. How many children have neither blue eyes nor blond hair?
A. 40
B. 26
C. 84
D. 70
E. 96
F. 12
Q2. How many numbers, at a minimum, should we choose at random from
S = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} in order to guarantee that the difference of
two of the chosen numbers is divisible by 4?
A. 2
B. 3
C. 4
D. 5
E. 6
F. None of the above
Transcribed Image Text:Q3. Suppose A = {1, 2,3,4}. Which of the following sets is the relation
R= {(a, b) | a+b is odd }?
A. R = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2, 4), (3, 3), (4,4)}
B. R= = {(1, 2), (1, 3), (1, 4), (2, 4)}}
C. R = {(1, 2), (2, 1), (1,3), (3, 1), (1, 4), (4, 1), (2, 4), (4, 2)}
D. R = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 4), (3, 3), (4, 4) }
E. R = = {(1, 2), (1, 4), (1, 3), (2, 4), (2, 2), (4, 4) }
= {(1, 2), (2, 1), (2, 3), (3, 2), (3, 4), (4, 3), (1, 4), (4, 1)}
F. R=
Q4. Letz and y be propositional variables. Which of the following propositions is not a
tautology?
A. xx
B. (x→y) V (y → x)
C. (x^x)
D.y → (x V-x)
E. x→→x
F. (y^-y) → x
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