1. Which of the following sentences are propositions? For those indicate the truth value. a. 123 is a prime number. b. O is an even number. e. What an impossible questiont 2. State the negation of each of the following statements. a. v2 is a rational number. b. O is not a negative integer, c. 111 is a prime number. 3. Let p: 17 is an odd number. 9: 9 is a prine number. State each of the following in words, and determine the truth value of each. a. -p vq b. p A-q c.- -p d.p - q e.qp 4. For statements p, q and, r use a truth table to show that each of the following pairs of statements is logically equivalent. a. (p A g) p and p= 4 b.p = (q v r) and -q (-p Vr) c. p (q v r) and (-r) - (p 4) d. p (q v r) and ((-r) A p) 5. For statements p, q, and r, show that the following compound statements are tautology. a.p (p v q) b.(p A (p q) → q c.(p q) A (a r))= (p =r) 6. Let p and q be statements, Which of the following implies that p v q is false? a. -p V -q is false. b. -p v q is true. c. -p A -g is true. d. p q is true. 7. Suppose that the statements p, q, r, and s are assigned the truth values T,.. and T, respectively. Find the truth value of each of the following statements. a. (p v q) vr b. p v (q v r) c. r (s A p) d. p (rs) c. p= (r V s) f. (p v r) (r A-s) g. (s p) (-p v s) h. (q A-s) (p s) 8. Construct the truth table for each of the following statements. a. p = (p = q) b. (p v q) (q v p) C.p- (q A r) d. (p q) (-p v q)
1. Which of the following sentences are propositions? For those indicate the truth value. a. 123 is a prime number. b. O is an even number. e. What an impossible questiont 2. State the negation of each of the following statements. a. v2 is a rational number. b. O is not a negative integer, c. 111 is a prime number. 3. Let p: 17 is an odd number. 9: 9 is a prine number. State each of the following in words, and determine the truth value of each. a. -p vq b. p A-q c.- -p d.p - q e.qp 4. For statements p, q and, r use a truth table to show that each of the following pairs of statements is logically equivalent. a. (p A g) p and p= 4 b.p = (q v r) and -q (-p Vr) c. p (q v r) and (-r) - (p 4) d. p (q v r) and ((-r) A p) 5. For statements p, q, and r, show that the following compound statements are tautology. a.p (p v q) b.(p A (p q) → q c.(p q) A (a r))= (p =r) 6. Let p and q be statements, Which of the following implies that p v q is false? a. -p V -q is false. b. -p v q is true. c. -p A -g is true. d. p q is true. 7. Suppose that the statements p, q, r, and s are assigned the truth values T,.. and T, respectively. Find the truth value of each of the following statements. a. (p v q) vr b. p v (q v r) c. r (s A p) d. p (rs) c. p= (r V s) f. (p v r) (r A-s) g. (s p) (-p v s) h. (q A-s) (p s) 8. Construct the truth table for each of the following statements. a. p = (p = q) b. (p v q) (q v p) C.p- (q A r) d. (p q) (-p v q)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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