Solutions to In class worksheet
For 1-5 let H: study hard and P: pass the course
1) If you study hard, you will pass this course.
2) If you pass the course then you studied hard. P H
3) Only if you study hard will you pass the course. P H
4) You will
Solutions and Example Problems using Quantifiers (Also Negate)
There are Hokies who do not like Wahoos.
H: set of all Hokies, P(X)=x does not like Wahoos
x x H
p ( x)
Everybody loves Science Fiction
P: set of all people, P(X)= x loves SF
x, x P p( x)
Math 2534 Solution Homework 4 Spring 2014
Problem 1:Put the following sentences in symbolic logic using a quantifier. Define the domain and the
single variable predicate for each statement
a) Most students read a book.
S is the set of all students (x is a
Examples of Valid and Invalid Arguments_
Determine if the following arguments are valid. Explain and justify your
conclusion. (You need to define all variables used_ Due to time I will not
define each one)
1) If Fred goes to the danc
Math 2534 Homework 3 (sec 2.2 -2.3)
Show all work and satisfy my homework requirements
Problem 1: Use Algebra of Logic to Prove the following:
Theorem ( p r ) (q r ) ( p q) r
( p r ) (q r )
( p r) ( q r)
( p q) r
If you wear Orange then I will wear Maroon
Which of the following statements are equivalent to the statement above?
Let O be the statement You wear orange.
Let M be the statement I will wear Maroon.
So the original statement is O M,
1) For me to wear maro
Solutions for Homework 1
1) Use Truth Tables to verify the following. Be very complete in truth table set up. Justify
the truth value of each individual part of the identities below.
[( p q) p] [ p ( p q)]
p q p q ( p q)
Math 2534 Solution Logic Algebra Homework due on Wednesday
Problem 1: Theorem 1: ( p q) ( p
Pr oof :
( p q) ( p r ) ( p q)
[( p q) ( p q)] ( p r )
[( p (q q)] ( p r )
[( p ( F )] ( p r )
[( p] ( p r )
[( p p) ( p r )
F ( p r )
Therefore ( p q)