Dr. Timo de Wolff
Institute of Mathematics
www.math.tamu.edu/~dewolff/Spring16/math302.html
MATH 302 – Discrete Mathematics – Section 501
Homework 4
Spring 2016
Due: Wednesday, February 24th, 2016, 4:10 pm.
When you hand in your homework, do not forget to add your name and your UIN.
Exercise 1. Let our domain be the set of objects and persons.
1. Introduce appropriate predicates and translate the following sentences into a proposition using quantifiers.
(a) “Italian pizza tastes better than every other pizza.” (“other” means “nonItalian” here).
(b) “If a breakfast is English, then it is made of baked beans and eggs.”
2. Translate the following propositions into a regular sentence using G(x) := “being
from Germany”, C(x) := “be a cake”, F (x, y) := “be more famous than”, P (x) :=
“be a person”, K(x, y) := “(so.) know(s) (so. / sth.)”.
¬∃x[G(x)∧C(x)∧F (x, Black Forest cake)]∧∀y : G(y)∧P (y) → K(y, Black Forest cake)
Exercise 2. For a set A the power set P(A) of A is the set of all subsets of A. E.g., for
A = {a, b} we have P(A) = {∅, {a}, {b}, {a, b}}.
1. Give all elements of P({a, 3, python}).
2. Power sets can be applied successively. Give all elements of P(P(P(∅))).
3. Show: If A ⊆ B, then P(A) ⊆ P(B).
Exercise 3. If a real number is not a rational number, then it is called irrational. Show
that for all x ∈ R holds: if x3 is irrational, then x is irrational.
Exercise 4. Show that the argument with premises “The tooth fairy is a real person” and
“The tooth fairy is not a real person” and conclusion “You can find gold at the end of the
rainbow” is a valid argument. Does this show that the conclusion is true? Explain your
answer.
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