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Discrete Mathematics
Suppose that in the world every pair of people either
(a) likes one another,
(b) dislikes one another, or
(c) is indifferent toward one another.
Prove that in any gathering of 17 people, there is a group of three people all of whom satisfy
one of conditions (a), (b) or (c).
(a) likes one another,
(b) dislikes one another, or
(c) is indifferent toward one another.
Prove that in any gathering of 17 people, there is a group of three people all of whom satisfy
one of conditions (a), (b) or (c).
Discrete Mathematics
Suppose that in the world every pair of people either
(a) likes one another,
(b) dislikes one another, or
(c) is indifferent toward one another.
Prove that in any gathering of 17 people, there is a group of three people all of whom satisfy
one of conditions (a), (b) or (c).
(a) likes one another,
(b) dislikes one another, or
(c) is indifferent toward one another.
Prove that in any gathering of 17 people, there is a group of three people all of whom satisfy
one of conditions (a), (b) or (c).
Discrete Mathematics
Give an example of a function with the following properties:
a. f: Z ⟶ Z that is one-to-one but not onto
b. f: Z ⟶ Z that is onto but not one-to-one
c. f: Z ⟶ N that is bijective
d. f: N ⟶Z that is bijective
e. f: Z ⟶ N that is one-to-one but not onto
f. f: N ⟶Z that is onto but not one-to-one
a. f: Z ⟶ Z that is one-to-one but not onto
b. f: Z ⟶ Z that is onto but not one-to-one
c. f: Z ⟶ N that is bijective
d. f: N ⟶Z that is bijective
e. f: Z ⟶ N that is one-to-one but not onto
f. f: N ⟶Z that is onto but not one-to-one
Discrete Mathematics
Write an algorithm that takes a list of integers a1,a2,…,an where and finds the largest and second-largest integer encountered.
Discrete Mathematics
A simple graph G is self complementry if G is isomorphic to G complement.Show that if G is self complementry,then v==0,1(mod4).
Discrete Mathematics
Prove that A - (A - B) : A intersectionB
Discrete Mathematics
let A be{1,2,3,4,11} let B be{2,4,5,6,9} and C be {1,3,7,8,10}
find 1.(A-B)-C
2.(A-C)-(B-C)
3.is (A-B)-C=(A-C)-(B-C)
find 1.(A-B)-C
2.(A-C)-(B-C)
3.is (A-B)-C=(A-C)-(B-C)
Discrete Mathematics
Evaluate the following with explanation:
A. 11^2012 mod 10
B. 29^205 mod 10
C. ⇩⇩⇩
20
Σ x!mod 5
x=1
D. Draw diagram for the following relation aRb iff a is congruent to b mod 3 on the set {0,1,2,3,4,5}
E. ⇩⇩⇩
5
Σ n(n!)
i=1
F.⇩⇩⇩
5
Σ i^3
i+1
G. Show that the sum of consecutive positive integers is equal to n/2(n+1),∀n∈ N.
A. 11^2012 mod 10
B. 29^205 mod 10
C. ⇩⇩⇩
20
Σ x!mod 5
x=1
D. Draw diagram for the following relation aRb iff a is congruent to b mod 3 on the set {0,1,2,3,4,5}
E. ⇩⇩⇩
5
Σ n(n!)
i=1
F.⇩⇩⇩
5
Σ i^3
i+1
G. Show that the sum of consecutive positive integers is equal to n/2(n+1),∀n∈ N.
Discrete Mathematics
Assignment 1
Pak Ali has purchased some stock in Global Warming, Inc. The details are as follows:
number of shares purchased was 1000 shares
Pak Ali has paid RM32.87 per share
Pak Ali paid his stock broker a commission that amounted to 2% of the amount he paid for the
stoc
A few days later, Pak Ali sold the stock. The details are as follows:
1000 shares was sold
the sale price was RM33.92 per share
Pak Ali paid his stock broker a commission that amounted to 2% of the amount he received for
the stock
The program should be able to display the following information:
the amount of money Pak ali paid for the stock
the amount of commission Pak Ali paid his broker for purchasing the stock
the amount that Pak Ali sold the stock for
the amount of commission Pak Ali paid his broker for selling the stock
the profit that Pak Ali made after selling his stock and paying the two commissions to his
broker
Attention
submission deadline is on Tuesday, October 2, during C++ class
what you have to submit
1) pseudocode of your program (hard copy)
2) your complete C++ source code (hard copy)
3) output of your C++ program (hard copy)
there is no need to send your C++ program file
write down your name and matric no
Example of how to submit your assignment (from today's lecture note).
1) Pseudocode
Ask the user to input the crate's length.
Ask the user to input the crate's width.
Ask the user to input the crate's height.
Calculate the crate's volume.
Calculate the cost of building the crate.
Calculate the customer's charge for the crate.
Calculate the profit made from the crate.
Display the crate's volume.
Display the cost of building the crate.
Display the customer's charge for the crate.
Display the profit made from the crate.
2) Complete C++ code
3) Program output
Pak Ali has purchased some stock in Global Warming, Inc. The details are as follows:
number of shares purchased was 1000 shares
Pak Ali has paid RM32.87 per share
Pak Ali paid his stock broker a commission that amounted to 2% of the amount he paid for the
stoc
A few days later, Pak Ali sold the stock. The details are as follows:
1000 shares was sold
the sale price was RM33.92 per share
Pak Ali paid his stock broker a commission that amounted to 2% of the amount he received for
the stock
The program should be able to display the following information:
the amount of money Pak ali paid for the stock
the amount of commission Pak Ali paid his broker for purchasing the stock
the amount that Pak Ali sold the stock for
the amount of commission Pak Ali paid his broker for selling the stock
the profit that Pak Ali made after selling his stock and paying the two commissions to his
broker
Attention
submission deadline is on Tuesday, October 2, during C++ class
what you have to submit
1) pseudocode of your program (hard copy)
2) your complete C++ source code (hard copy)
3) output of your C++ program (hard copy)
there is no need to send your C++ program file
write down your name and matric no
Example of how to submit your assignment (from today's lecture note).
1) Pseudocode
Ask the user to input the crate's length.
Ask the user to input the crate's width.
Ask the user to input the crate's height.
Calculate the crate's volume.
Calculate the cost of building the crate.
Calculate the customer's charge for the crate.
Calculate the profit made from the crate.
Display the crate's volume.
Display the cost of building the crate.
Display the customer's charge for the crate.
Display the profit made from the crate.
2) Complete C++ code
3) Program output
Discrete Mathematics
how many arrangements of six 0s
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#340153 on Dec 2023
#340153 on Dec 2023