DACS 2101 – Discrete Structures
In-Class Exercises 1
1-
Let p, q, and r be the propositions
p :You get an A on the final exam.
q :You do every exercise in this book.
r :You get an A in this class.
Write these propositions using p, q, and r and logical connectives (including negations).
a) You get an A in this class, and you do every exercise in this book.
b) You get an A in this class, or you do every exercise in this book.
c) You get an A in this class, but you do not do every exercise in this book.
d) You do not get an A on the final exam.
e) You do not get an A on the final exam but you get an A in this class.
f) You get an A on the final, you do every exercise in this book, and you get an A in this
class.
2-
Construct a truth table for (p ˄ q) ˅ r.
3-
Construct a truth table for (¬p ˄ q) ˅ (r ˅¬s).
4-
XOR:
a. Recall the truth table of p⊕q
b. Construct the truth table of (p⊕q)⊕r
c. Construct the truth table of (p⊕q)⊕(r⊕s)
d. What is the general rule for the truth value of XOR of n propositional variables
where n is larger than or equal than 2?
e. Is ¬p⊕¬q the negation of p⊕q? Justify your answer.