Homework Answers

1. Use the truth tables to verify these equivalence

suppose the production cost is R18 925, labour cost is R1245 and equipment renting fee of R250, determine the number of devices produced

1.Find the Domain and Range of the following functions if 𝑓: 𝑅 → 𝑅 i) 𝑓(𝑥) = 12 + 𝑙𝑜𝑔 (1 − 𝑥^2 ) ii) 𝑓(𝑥) = 𝑥^2 +1/𝑥^2 +5

2. Find if the functions are surjective, injective and bijective if 𝑓: 𝑅 → 𝑅 i) 𝑓(𝑥) = 𝑥^5 + 5 ii) 𝑓(𝑥) = 𝑒^4𝑥 

A large logistic manufacturing company has 100 employees specializing in different machines. From them, 20 are proficient in machine P , 45 in machine Q , 30 in machine R , 1 in machine P and Q , 6 in machine Q and R , 5 in machine R and P , and just 1 specialist in all three machines. i) Determine how many of them only specialize in machine Q. ii) And how many of them do not specialize in any of the machines. 

Determine the Power set of 𝐴 × 𝐵 if 𝐴 = { 7, 8 } and 𝐵 = { 𝑎, 𝑏 }

Six women and five men walk into an

appliance store at the same time. There are five

salesperson available to help them.Find the

probability that a salesperson will first help at

least 2 women.