Chapter 1.1, Problem 33P

1. 2. Show that the following are not logically equivalent by finding a counterexample: (p^q) →r and (db) V (d←d) Show that the following is not a contradiction by finding a counterexample: (pV-q) AqA (pv¬q Vr) 3. Here is a purported proof that (pq) ^ (q → p) = F: (db) v (bd) = (db) v (bd) =(qVp) A (g→p) = (¬¬q V ¬p) ^ (q→ p) (db) V (db) = =¬(a→p)^(a→p) = (gp) ^¬(a → p) =F (a) Show that (pq) ^ (q→p) and F are not logically equivalent by finding a counterex- ample. (b) Identify the error(s) in this proof and justify why they are errors. Justify the other steps with their corresponding laws of propositional logic.

5 Show by multiplying matrices that the following equation represents an ellipse: 5 - -7 I (x)(3)()=30. y) 7 7)

No chatgpt pls

1: Stanley Smothers receives tips from customers as a standard component of his weekly pay. He was paid $5.10/hour by his employer and received $305 in tips during the most recent 41-hour workweek. Gross Pay = $ 2: Arnold Weiner receives tips from customers as a standard component of his weekly pay. He was paid $4.40/hour by his employer and received $188 in tips during the most recent 47-hour workweek. Gross Pay = $ 3: Katherine Shaw receives tips from customers as a standard component of her weekly pay. She was paid $2.20/hour by her employer and received $553 in tips during the most recent 56-hour workweek. Gross Pay = $ 4: Tracey Houseman receives tips from customers as a standard component of her weekly pay. She was paid $3.90/hour by her employer and received $472 in tips during the most recent 45-hour workweek. Gross Pay = $

8 √x+...∞ If, y = x + √ x + √x + √x +. then y(2) =? 00

8 √x+...∞ If, y = x + √ x + √x + √x +. then y(2) =? 00

How many different passwords are there that contain only digits and lower-case letters and satisfy the given restrictions? (a) Length is 6 and the password must contain at least one digit. (b) Length is 6 and the password must contain at least one digit and at least one letter.

1: Neil Mitchell earns $11/hour. During the most recent week, he received a discretionary bonus of $7,200 and worked 43 hours. Gross Pay: $ 7,689.50 2: Francine Palmer earns $7.90/hour. During the most recent week, she received a nondiscretionary bonus of $2,450 and worked 45 hours. Gross Pay: $ 2,825.25 3: Martin Green earns $11.10/hour. During the most recent week, he received a nondiscretionary bonus of $1,360 and worked 51 hours. Gross Pay: $ 1,987.15 4: Melvin Waxman earns $17.60/hour. During the most recent week, he received a nondiscretionary bonus of $440 and worked 56 hours. Gross Pay: $ 1,425.60

1: Kevin Williams earns a weekly wage of $740. During the most recent week, he worked 42 hours. Regular Wage Rate = $ 18.50 Overtime Wage Rate = $ 27.75 2: Charles Joyner earns a biweekly wage of $2,720. During the most recent week, he worked 45 hours. Regular Wage Rate = $ Overtime Wage Rate = $_ 34.00 51.00 3: Julio Valdez earns an annual salary of $81,000. During the most recent week, he worked 44 hours. Regular Wage Rate = $ Overtime Wage Rate = $ 38.94 58.41 4: Bridget Stein earns a monthly salary of $6,200. During the most recent week, she worked 56 hours. Regular Wage Rate = $ 27.50 Overtime Wage Rate = $ 41.25 5: Betsy Cranston earns a semimonthly salary of $2,200. During the most recent week, she worked 49 hours. Regular Wage Rate = $ Overtime Wage Rate = $_ 1,100.00 41.25