Elements of Discrete Mathematics G22.2340-001 Second Problem Set
June 17, 2009
Due by June 30. Collaboration is allowed; please mention your collaborators. Before embarking on any proof, rst write what it is that you want to prove in a formal way using wh
Elements of Discrete Mathematics G22.2340-001 First Problem Set
June 2, 2009
Due by June 16. Collaboration is allowed; please mention your collaborators. Problem 1 Given that p, q and r are statement variables, use any method you know to prove which of th
Predicates
. are "parameterized" propositions.
- functions that take a value (from some domain) and then they have
a truth value.
i.e. Statements like "x+1=3" are examples of predicates, and we can
write this predicate as p(x).
you can have predicates tha
Practice Final Exam 2010
Please write your name at the top of this page. There are no *trick* questions on this exam, but
approach each problem with an open mind. Please keep track of the time, and good luck.
1. (Very Short answer)
(a) Let A be the set cf
Inference rules for quantifiers
Often one mixes quantified and unquantified statements, then we can play the same
"find what rules we can apply" game as before.
(exists) x (C(x) ^ ~B(x)
(forall) x (C(x) -> P(X)
-(exists) x (P(x) ^ ~B(x)
1. (exists) x (C(x
Truth tables.
A logical expression, such as (p AND q) or r), has a truth value that depends on the
truth values of the propositions (the p's, q's, and r's) that make up the expression. A
truth table is an organized way of writing down the truth value of a
Tautology
When a propositional expression is equivalent to TRUE, we call it a TAUTOLOGY:
in a tautology, every possible possible way of assigning truth values to the
propositions leads to an expression which is true.
Q -> (~P v Q) <=> T
Contradictions
Whe
Sample Final Exam Questions
The nal exam will focus on the following topics, questions may dened in terms of logical formulas,
set-builder notation, functions, etc. Proofs about these topics may require proof by contradiction
or induction. Your test will
Propositional Equivalence
So far, we've defined propositions, defined how to make compound expressions with
connectives, talked about how to find logically equivalent propositions, and talked
about quantifying statements so that we can make statements abo
Elements of Discrete Mathematics G22.2340-001 Fourth Problem Set
July 16, 2009
Due by July 28. Collaboration is allowed; please mention your collaborators. Problem 1 How many strings of six lowercase letters from the English alphabet contain (a) the lette
Elements of Discrete Mathematics G22.2340-001 Third Problem Set
July 1, 2009
Due by July 14. Collaboration is allowed; please mention your collaborators. Problem 1 Find f (1), f (2), f (3), f (4) and f (5) if f (n) is dened recursively by f (0) = 3 and fo