Math 310
Exam 1 - Practice Problems
1. Translate the following English statements into symbolic form (use propositional sentences).
(a) I will not pass this class unless I go to class every day and do
Math 310: Discrete Mathematics
Some Important Logical Equivalences
Equivalence
pTp
pFp
pT T
pF F
ppp
ppp
( p) p
pq qp
pq qp
(p q ) r p (q r )
(p q ) r p (q r )
p (q r ) (p q ) ( p r )
p (q r ) (p q )
Math 310
Quiz 1
01/13/2014
Name:
1. Charles Lutwidge Dodgson was a writer, mathematician, logician.
(a) Give the name of the city where Charles Lutwidge Dodgson was born and the year he was born.
(b)
Math 310
Solutions to Selected Problems from HW #6
2.1 #16 Find two sets such that A B and A B .
Solution:
First, we should note that to have any chance of A being both an element of B and a subset of
Math 310
Solutions to Selected Problems from HW 2
Section 1.2 #41: This question asks us to construct a logical expression involving p, q , and r which is true when exactly
two of these variables are
Math 310
Solutions to HW 1.1
Problem #45: Each inhabitant of a remote village always tells the truth or always lies. A villager will only give a Yes
or a No response to a question a tourist asks. Supp
Math 310
Exam 2
Name:
Instructions: You will have 55 minutes to complete this exam. The credit given on each problem will be
proportional to the amount of correct work shown. Answers without supportin
Math 310
Gateway Quiz 2 - Version 1
Name:
1. (8 points) Suppose that r is a non-zero rational number. Use the denition of rational to prove that rk is
rational for any k Z.
First, apologies for the mi
Math 310
Exam 1 - Version 1
Name:
Instructions: You will have 55 minutes to complete this exam. The credit given on each problem will
be proportional to the amount of correct work shown. Answers witho
Math 310
Gateway Quiz 1 - Version 1
Solutions
Name:
1. (8 points) Write the negation of the following symbolic statement. Your answer should be written
in fully simplied form (i.e. so that no negation
Math 310
Exam 2 - Practice Problems
1. Prove that there is an integer m such that m3 > 1010 . Is your proof constructive or non-constructive?
2. Prove that given any two rational numbers p < q , there
Math 310
Exam 2 - Practice Problem Solutions
1. Prove that there is an integer m such that m3 > 1010 . Is your proof constructive or non-constructive?
Let m = 2200. Then m3 = (2200)3 = 10, 648, 000, 0
Math 310
Exam 1 - Practice Problem Solutions
1. Translate the following English statements into symbolic form (use propositional sentences).
(a) I will not pass this class unless I go to class every d
Math 310
Logic and Truth Tables
Denition: A proposition is a declarative sentence that is either true or false (but not both). That is, a statement ends
up having one of two possible truth values:
If