CMSC 150 Assignment 3 Answer Sheet
Name: Woo Choi
1: Prove that the difference of two odd integers is even. Give a justification at each step.
Suppose that x and y are odd.
x= 2n+1 for all integers n
Homework 1
1. Which of the following sentences are logical statements? (20 points, 4 parts- 5 points
each)
a. If x even divides y, then x is a factor of y
b. If John does well in discrete math, then h
CMSC 150 Section 6380 Fall 2017 Assignment 2 Answer Sheet
Name:
1: Translate the following English sentences into statements of predicate calculus.
a. All programmers enjoy discrete mathematics.
x: pr
Andrew Sheetz
CMSC 150 (6381)
Homework 1
1. Which of the following sentences are logical statements? (20 points, 4 parts- 5 points each)
a. If x even divides y, then x is a factor of y
Both statements
Homework 5
1. Enumerate the elements of the following relations from the set A of positive integers less
than or equal to 10 to the set B of positive integers less than or equal to 30. (20 points, 2
p
Homework 2
1. Translate the following English sentences into statements of predicate calculus. (20 points, 4
parts 5 points each)
a. All programmers enjoy discrete mathematics
( p) = all programmers
E
Homework 4
1. Enumerate the elements of the following sets: (20 points, 2 parts- 10 points each)
a. cfw_x: x is an odd positive integer less than 13
cfw_1, 3, 5, 7, 9, 11
cfw_x Z | x = 2k +1 ^ 0 < x <
Homework 6
1. Determine whether each of the following functions is 1-to-1 and whether it is onto. Assume
the domain and co-domain is Z, the integers. Explain your answers. (20 points, 2 parts 10
point
Homework 3
1. Prove that the difference of two odd integers is even. Give a justification at each
step. (20 points)
a, b are integers
( a)( b) [O(a)
O( ) = is odd
E ( ) = is even
O(b)
E(a-b)]
a = 2k1
Homework 3
. Prove that the dierence of two odd integers is even. Give a justication at each step. (20
points) M h z? + I (and m if: ( Lag 19, 4A, ilrar ate/49' .Jeed
710! 11! :(z?+i>(11a: wig 2K? 42)
Even
Homework 2
1. Translate the following English sentences into statements of predicate calculus. (20
points, 4 parts - 5 points each)
a. All progr ers enjoy discrete mathematics
cfw_V0590 4&[6] 7
F
1&7 ink
1. Enumerate the elements of the following sets: (20 points, 2 parts 10 points each)
a. cfw_x: xis anodd positive integer less than 13 g l , 2 S" 7, 9 I Ir
b. cfw_y: y is a positive integer th
Homework 4
1. Enumerate the elements of the following sets: (20 points, 2 parts- 10 points each)
a. cfw_x: x is an odd positive integer less than 13
b. cfw_y: y is a positive integer that is a multipl
Homework 3
1. Prove that the difference of two odd integers is even. Give a justification at each step. (20
points)
2. Prove that the sum of any two rational numbers is a rational number. Give a justi
Caitlyn Morgan
September 17, 2017
Homework 4
1. Enumerate the elements of the following sets:
a. cfw_x: x is an odd positive integer less than 13
cfw_1,3,5,7,9,11
b. cfw_y: y is a positive integer tha
Caitlyn Morgan
September 9, 2017
1. Prove that the difference of two odd integers is even. Give a justification at each step.
Let p = 2m +1 and q = 2n+1, where p+q are both odd integers.
Then p q = 2m
Caitlyn Morgan
August 26, 2017
Homework 1
1. Which of the following are logical statements?
a. If x evenly divides y, then x is a factor of y.
True. For example, If I divide 4 by 2 then I receive an a
Caitlyn Morgan
September 3, 2017
Homework #2
1. Translate the following English sentences into statements of predicate calculus.
a. All programmers enjoy discrete mathematics
(x) [P(x)P(y)]
where P(x)
Corrected answers are in red
CMSC 150 Section 6380 Spring 2017 Assignment 1 Answer Sheet
Name:
1: Which of the following sentences are logical statements?
a: If x even divides y, then x is a factor of
Corrected answers in red
CMSC 150 Section 6380 Spring 2017 Assignment 2 Answer Sheet
Name:
1: Translate the following English sentences into statements of predicate calculus.
a. All programmers enjoy
This homework received 100% from the professor
CMSC 150 Section 6380 Spring 2017 Assignment 6 Answer Sheet
Name:
1: Determine whether each of the following functions is 1-to-1 and whether it is onto.
This homework received 100% from the professor
CMSC 150 Section 6380 Spring 2017 Assignment 3 Answer Sheet
Name:
1: Prove that the difference of two odd integers is even. Give a justification
at each
This homework received 100% from the professor
CMSC 150 Section 6380 Spring 2017 Assignment 7 Answer Sheet
Name:
1: Calculate the number of integers divisible by 4 between 50 and 500, inclusive.
N = 4
Corrected answers are in red
CMSC 150 Section 6380 Spring 2017 Final Exam Answer Sheet
Name:
1: For each the following groups of sets, determine whether they form a partition for the set of
integers.
Corrected answers are in red
CMSC 150 Section 6380 Spring 2017 Assignment 5 Answer Sheet
Name:
1: Enumerate the elements of the following relations from the set A of positive integers less than
or equ
This homework received 100% from professor
CMSC 150 Section 6380 Spring 2017 Assignment 4 Answer Sheet
Name:
1: Enumerate the elements of the following sets:
a. cfw_x: x is an odd positive integer les
CMSC 150 Section 6380 Spring 2017 Assignment 4 Answer Sheet
Name:
1: Enumerate the elements of the following sets:
a. cfw_x: x is an odd positive integer less than 13
cfw_1, 3, 5, 7, 11
b. cfw_y: y is
CMSC 150
Homework 1
1. Whichofthefollowingsentencesarelogicalstatements?
a.
Ifxevendividesy,thenxisafactorofy
b.
IfJohndoeswellindiscretemath,thenhewillbeanexcellentprogrammer
c.
2istheonlyevenprimenu
CMIS 150
Homework 4
1. Enumerate the elements of the following sets:
a. cfw_x: x is an odd positive integer less than 13
cfw_1, 3, 5, 7, 9, 11
b. cfw_y: y is a positive integer that is a multiple of 4