Examples of proofs (by type)
(Theorems to be proved in class, and required denitions)
Direct proof
Denition 1 An integer n is called odd if n = 2k + 1 for some integer k , and is called
even if n = 2m for some integer m.
Theorem 2 If n is an odd integer,
Arguments
An argument is a set of propositions in which one (called the conclusion) is
claimed to follow from the others (called the hypotheses or premises). In other
words, an argument is a proposition of the form
(P1 P2 . . . Pk ) C,
where P1 , P2 , .
DGD (circle):
TA (circle):
Marks:
1
Stan
2
Last name:
Yue
/25
First name:
Student number:
MAT 1348 First Homework Assignment Due Jan. 22, 2014 at 11:20am
Instructions: Show all relevant work to receive full credit. Submit a nished product, not
a draft. Yo
A Method of Solving Knights-And-Knaves Questions
There is an island far o in the Pacic, called the Island of Knights and Knaves. On
this island, there are people called knights, who always tell the truth, and people called
knaves, who always lie. The two
Examples of arguments
1. P1 : If Socrates is human, then he is mortal.
P2 : Socrates is human.
C: Socrates is mortal.
2. P1 : If I eat spicy food, I have strange dreams.
P2 : I do not have strange dreams.
C: I do not eat spicy food.
3. What conclusion(s)
Truth Trees
Like truth tables, truth trees are used to determine all truth assignments of the
propositional variables (atomic propositions) that make a compound proposition
true. Unlike a truth table, whose size grows exponentially with the number of
pro