Search & Filtering
Solve the following problems following Polya’s Four Step Method and employing the
different strategies discussed. Write the problem and present the solution neatly
and organized.
a. Frosia delivers prescriptions for the local pharmacy. On Tuesday, she delivered 5/9
of the prescriptions already in the delivery van and then 3/4of the remaining
prescriptions. After picking up 10 more prescriptions at the store, she delivered 2/3 of
those she had with her. She then picked up an additional 12 prescriptions and delivered 7/8 of those she had in the van. Finally, she up 3 more and then delivered the remaining 5 prescriptions. How many prescriptions did she deliver?
b. Joyce invited 17 friends to a dinner party at her house last Friday evening. She
gave each guest a card with a number from 2 through 18, reserving number 1 for
herself. When she had everyone paired off at the dinner table, she noticed that
the sum of each couple’s numbers was perfect square. What number did Joyce’s
partner have?
Draw the Venn diagrams for each of these combinations of the sets A, B, and C. Shade
the region(s) corresponding to the given set expressions.
a. (A ∪ B) ∩ C
b. (𝐴̅∩ B) ∩ 𝐶̅
c. (A ∩ 𝐶̅) ∪ 𝐵̅
d. A ∩ (B ∩ 𝐶̅)
Let P = {(1, 4),(3, 5),(4, 1)}, Q = {(1, 5),(2, 2),(3, 4),(5, 2)} and R ={(4, 4),(2, 1),(5, 3),(3, 4)}.
Find P ◦ Q ◦ R
Discussion Assignment
Let f(x)=\sqrt(x) with f: \mathbb{R} \to \mathbb{R}. Discuss the properties of f. Is it injective, surjective, bijective, is it a function? Why or why not? Under what conditions change this?
Explain using examples.
Let 𝑝, 𝑞 and 𝑟 be the propositions:
𝑝: You have the flu
𝑞: You miss the final examination
𝑟: You pass the course
Express each of the following propositions as an English sentence.
i) ¬𝑞 ↔ 𝑟 [2 Marks]
ii) (𝑝 → ¬𝑟)˅(𝑞 → ¬𝑟) [2 Marks]
p: I study hard on discrete mathematics
q: I play football everyday
r: I will get a good result for the examination
Show, by the use of the truth table/matrix, that the statement (p v q) v [( ¬p) ∧ (¬q)] is a tautology.
5. What is the negation of each of these propositions? a) Mei has an MP3 player. b) There is no pollution in New Jersey. c) 2 + 1 = 3. d) The summer in Maine is hot and sunny.
Show that the polynomial function Z +×Z +→Z + with f(m, n) = (m + n − 2)(m + n − 1)/2 + m is one-to-one and onto
IA∘R=R=R∘IA.
