We can have as many variables as we like
Negation
Sometimes , we want to negate predicates and quantifires
“There exists an x so P(x) is false
To show something is false , we can show the negation is True
Summary:
•
Predicates of 1,2 variables
•
exis
Determine if the following statement is true or false if false provide a counter
example
Translate from logic to plain language
A) every element of s is an integer
B)there is some elements of S that is an integer
C) all odd numbers are integers
D) at least one odd number is an integer
A)
Every possible natural number , I can
then find an integer so that x > y
There exists some natural’ number so that z<y for
every intiger y
Week 2 lecture 2
Intro to Proofs
Notice this changes the initial statement to not (B) implies not (A) and then proves
directly
We have shown that. Is odd when x is
odd. So by the contrapositive , if
Then x is even.
We have shown by the contrapositive that if
Is odd then x is even
Since we have shown the implication in both directions it is true that x is even iff