6. (4 marks) Write down the negation of each of the following statements. Then determine whether...
2. Let D-E-(-2,-10,1,2). write negations for each of the following statements and determine which is true, the original or the negation. Vx e D,3y E E such that xy 2 y True: OriginalNesgation a. b. 3x E D such that Vy E E, x y True: Original Negation
For statements 3-4 a) Write a negation of the statement in symbolic form b) Write each statement and negation as a meaningful English sentence. For statements 3-4 a) Write a negation of the statement in symbolic form b) Write each statement and negation as a meaningful English sentence.
Discrete Math in the final answer) 6. Write the negation of the following statements (without using (a). Un e Z+, 3p EP, n3 <p < (n + 1)3. (b). Vce R+,3K EZ+, Vn e Z, n > K → n n+100 < c.
EXERCISES 6 Write and simplify the negation to the following le statements a) 3x<x2+1< 5 W . x>2 Vy<3 6) $9xty >3 .01.29 Izs1. (x-y< L da ih abzc ad bad c) 4x<1e y>2 acd d) a<b<ce bread 2 i) { x=1 Vy <3 e) x+1 <4 K x 2 <24 <3x+S Iz>y>x. f) ab. (cs d & cze) g) { x< 1 v { x=3 • lyce Tyzl
2. For the following quantified statement, (a) Write the negation of the statement. (Don't simply put a in front of the statement. Actually rewrite to get a quantified statement that is equivalent to the negation.) Original Statement: Vr e Z. By e Z, az eZ: 72 = y2 + z2. Negation of the original statement: (b) Decide whether the original statement is true or the negation of the original statement is true. Include some brief justification of how you know.
Problem 2. For the following statements, write down whether true or false (No justification needed, and for ease of grading, please make it clear what is) (1) (a) xE (b) х€ {{x}} (c) x}€{{x}} (d) } E (2) (a) C 1,2,3 (b) E {1,2,3 (c)E P({1,2,3} (d) n0 (3) (a) 1,2,3 (b) {1,2,3} с {1, 2, 3} (c) An0 (d) AU A (4) a) ZnZ = Z (b) ZUZ 22 your answer Problem 3. List the elements of the following...
For each of the following statements, decide whether or not it is true and write down a clear and convincing explanation for your decision. Some of these are harder than others, and one of them is not known to anyone (c) There are non-zero integers m and n such that m(e + 7) = n. (Here, it is the number for which cos(TT) = -1, and e is the number such that f(x) = e is its own derivative.)
16 pts) #4. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) A statement is a sentence that is true. ________(b) In logic, p q refers to the "inclusive or, " true when either p or q or both are true. ________(c) The phrase "not p and not q" means "not both p and q." ________(d) The conditional statement p q is true if p is false. ________(e) The negation of p q is p ~q. #5....
Rewrite the following statement so that negations appear only within predicates (i.e., no negation or not is outside a quantifier or a compound statement using logical operators/connectives). Please write it clearly and show every step! V ((Vy32 -P(x, y, z)) 4 (3 z Vy R(x, y, z)))
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0. ________(b) m, n in N, 5m 2n is in N. ________(c) x in R, if |x − 2| < 3, then |x| < 5. #8. For each statement, (i) write the statement in logical form with appropriate variables and quantifiers, (ii) write the negation in logical form, and (iii) write the negation in a clearly worded unambiguous English sentence....