CSC 230 Discrete Structures

How many rows appear in a truth table for each of these compound propositions?

a. (pr)(qs)

b. (prt)(qt)

Whatistheinverseofpq?

What is the converse of pq?

What is the contrapositive of pq?

Which of the following are logically equivalent? (multiple choice)

A conditional and its inverse

A conditional and it converse

A conditional and its contrapositive

The inverse of a conditional and its converse

Show that (pq) and pq are logically equivalent.

Show the truth table for (p q) (p q)

Show that (pq)(pr)(qr) is a tautology.

Show that(pq)r and p(qr) are not logically equivalent.

10.For each of the following logical equivalences, identify the equivalence law: a. (pq)pq

b. pqqp c. p(qr)(pq)(pr) d. (pq)rp(qr)

11.Apply DeMorgans Law to find the logical equivalence of

a. p q b. p(qr)

12.Let P(x) be the statement x = x2. If the domain consists of the integers, what are these truth values?

a. P(0) b. P(1) c. P(2) d. P(1) e. xP(x) f. xP(x)

13.Determine the truth value of each of these statements if the domain consists of all real numbers.

x(x3 = 1)

x(x4 < x2)

x((x)2 = x2)

x(2x > x)

14.Suppose that the domain of the propositional function P(x) consists of the integers 0, 1, 2, and 3. Write out each of these propositions using disjunctions, conjunctions, and negations.

a. xP(x) b. xP(x)

c. xP(x) d. xP(x) e. xP(x) f. xP(x)

15.Show that the argument form with Premises: (r s), p s, p q

Conclusion: q is valid by using rules of inference.