(a) (b) Write the negation of the following statement without using any negative words ("no", "not", "none", etc.): "An employee at a Starbucks in Manitoba has a bookshelf on which every book has the property that on every odd-numbered page, if the second-last word has four or more letters, then the first and last letter of that word come alphabetically after M.” neously. - Find an example of a subset ACR that has all of the following properties simulta- A is not empty. bR such that Vx E A, b ≤ x. - Vy Є A, 3x Є A such that x 0}, Before stating the next problem, we need to make some definitions. We write I and say that a function ƒ : I → I is strictly increasing if Vx, y Є I with x > y we have f(x) > f(y).

Let p = "2 is a factor of n," q = "3 is a factor of n," and r= "6 is a factor of n." (a) Let Statement A be "If 2 is a factor of n and 3 is a factor of n, then 6 is a factor of n." Which of the following expresses Statement A in symbolic form? Opva Opnar Opvar O~P~g →r Opn~g (b) Let Statement B be "2 is not a factor of n, or 3 is not a factor of n, or 6 is a factor of n." Which of the following expresses Statement B in symbolic form? ONDANG Ar O p V NT O~Par ONDANG →r O ~p V NQ vr (c) Fill in the values in the truth table for Statements A and B. par TTT NP ? ♥ T FT ? ✓ FTF TTF ??✔ TFF FT T ? ♥ ? ✓ Ng ? ✓ ? ✓ ? ✓ ?v ? ✓ ? ✔ FFT ??✔ F FF ? ✓ ?✔ P^q ? ✔ ? ✓ ? V ? V ? ✓ Pлq→r NP V Nq Vr ? ✓ ?✔ ? ✓ ? ✓ ? ✔ ? ✔ ? V ? ✓ ?v ?v ?v ? ✓ Are Statements A and B logically equivalent? Fill in the blanks in the sentences below to justify your answer. The truth table shows that p^grand ~p V ~g vr--Select--- ✓have the same truth values. Therefore, Statements A and B ---Select-- logically equivalent.

3. Write the converse, inverse, contrapositive, and negation of the following statement. "If Sandra finishes her works, she will go to the basketball game.' Converse: Inverse: Contrapositive: Negation:

(1) What is the negation of the following statement: "n is divisible by 6 and n is divisible by both 2 and 3." A. n is not divisible by 6 or n is divisible by both 2 and 3.B. n is divisible by 6 or n is not divisible by both 2 and 3.C. n is not divisible by 6 and n is not divisible by both 2 and 3.D. n is divisible by 6 and n is divisible by both 2 and 3.E. n is not divisible by 6 or n is not divisible by both 2 and 3.F. n is not divisible by 6 and n is divisible by both 2 and 3.G. n is divisible by 6 or n is divisible by both 2 and 3.H. n is divisible by 6 and n is not divisible by both 2 and 3. (2) What is the negation of the following statement: "I exercise or I feel tired." A. I don't exercise or I feel tired.B. I exercise or I feel tired.C. I exercise or I feel envigorated.D. I don't exercise or I feel envigorated.E. I exercise and I feel tired.F. I exercise and I feel envigorated.G. I don't exercise and I feel envigorated.H. I don't exercise and I feel tired.

Let p and q represent the following statements. p: You study hard. q: You graduate with honors. Write the following statement in symbolic form: "You study hard, but you still don't graduate with honors." To enter your response, select the appropriate statement in each of the dropdown boxes, and select the appropriate operation in the middle. If only one statement is used, select "none" for the operation in the middle and the statement in the second dropdown box. Be sure to enter the statements in the same order as in the given sentence. DO A O V Onone (Select an answer ?

Which of the following is the negation of ' If Tom is Ann's father, then Jim is her uncle." ?

Which statement is the negation of nobody wants to go outside today

Give the logical negation of “All doorbells ring” a. Some doorbells do not ring. b. No doorbells knock. c. No doorbells ring. d. Some doorbells ring.

Let p, q, and r represent the following simple statements. p: I eat bananas. q: It is Tuesday. r:I get an A. Write the following compound statement in its symbolic form. I eat bananas and it is Tuesday, or I get an A. The symbolic form is

Give the negations: All cars run on a gasoline