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CHAPTER 2 Formal Logic
2. Write in symbolic form the statement "Claudia will sail in the regatta if the crew is
ready and the weather is fair."
3. Write the converse, inverse, and contrapositive of the statement "If Sally finishes her
work, she will go to the basketball game."
4. What inference rule applies to the following?
Joe wrote a program in C, or George wrote a program in Java. If Joe wrote a program in
C, then the problem was solved. If George wrote a program in Java, then the problem
was solved.
(a) Contrapositive
(b) Proof by contradiction
(c) Proof by cases
(d) None of the above
5. What is the truth value that will be computed by the formula represented by the
expression tree shown if I (p) = T, I (q) = F, I (r) = T, and I (s) = F in an interpretation I?
(-'(p A q) --ý r) <-* -4 (r-- s)
-(p A q)--- r
(r- s)
-(r(pAq)
r r- s
pAq
r
S
p
q
6. What is the value of the formula represented by the expression tree in Exercise 5 given
the interpretation I(p) = T, I(q) = F, I(r) = T, and I(s) = T.
7. Write the following condition in an if... then with the negations incorporated into the
conditions themselves:
If NOT ((x < 3) OR (y > 2)), then
8. Construct a truth table for the proposition -- (p A q).
9. Using the conjunctive normal form, identify values for which the statement
-(-'(p V q) A (-p V q))
is true.
10. Find the DNF for the statement
((-'p A q) V r) A (-'q v -r)
2.9.3 Review Questions
1. Construct a truth table for the statement -'(p V q) V -(p A q).
2. Construct a truth table for the statement -- (p A q) A (p V -q).
3. For which truth values does the statement -'(p V -- q) have a truth value TRUE?