150 CHAPTER 2 Formal Logic
- Write in symbolic form the statement "Claudia will sail in the regatta if the crew is
ready and the weather is fair." - Write the converse, inverse, and contrapositive of the statement "If Sally finishes her
work, she will go to the basketball game." - 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 - 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 inter-
pretation I?
(-'(p A q) --ý r) <-* -4 (r-- s)
-(p A q)--- r (r- s)-(r(pAq) r r- spAq r Sp q- 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.
- Write the following condition in an if... then with the negations incorporated into the
conditions themselves:
If NOT ((x < 3) OR (y > 2)), then - Construct a truth table for the proposition -- (p A q).
- Using the conjunctive normal form, identify values for which the statement
-(-'(p V q) A (-p V q))
is true.- 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).
- Construct a truth table for the statement -- (p A q) A (p V -q).