Discrete Mathematics Answers

~(~p^q) ^(pvq) =p

Use POLYA'S FOUR-STEP PROBLEM SOLVING STRATEGY to solve the problems.

1.  Layla is going to buy 30 multi-vitamin capsules, some P10 and some P18. If she has P340, what is the maximum number of P18 multi-vitamin capsules she can buy? (HINT: Use inequality)
2. Yesterday, Ling got confused about which day of the week it was. Whenever they go to long vacation, he forgets. Johnson said its Friday, but Roger said its Saturday. Ling asked what day is it tomorrow? Roger said its Monday, while Johnson said its Tuesday. Ling asked again, what day has it yesterday? Johnson said Wednesday, while Roger said its Thursday. Johnson and Roger have given one correct answer and two wrong answers. What day is it today? 

Let R be the relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by the rule

if the integer (a – b) is divisible by 4. List the elements of R and its

inverse?

Suppose p is the statement 'There are 1,000 meters in one kilometer' and q is the statement 'You will give me a cake.' Select the correct symbolization for the statement 'There are 1,000 meters in one kilometer or you will not give me a cake'.

b)                 Let 𝑆 = {𝑎,      𝑏,        𝑐} and 𝑅 = {(𝑎, 𝑎),     (𝑏, 𝑏), (𝑐, 𝑐),  (𝑏, 𝑐), (𝑐, 𝑏)}, find [𝑎], [𝑏]                                   

           and [𝑐] (that is the equivalent class of a, b, and c). Hence or otherwise find the set of the equivalent class of 𝑎, 𝑏 and 𝑐?  

Find all combinations of truth values for p, q and r for which the statement ¬p ↔ (q ∧ ¬(p → r)) is true

For any rational numbers r and s, 2r + 3s is rational.

Consider Premises: If Claghorn has wide support, then he’ll be asked to run for the senate. If Claghorn yells “Eureka” in Iowa, he will not be asked to run for the senate. Claghorn yells “Eureka” in Iowa. Conclusion: Claghorn does not have wide support. Determine whether the conclusion follows logically from the premises. Explain by representing the statements symbolically and using rules of inference

On the basis of 5 years of data the following probability function for a company’s

weekly demand for wool was:

Amount of wool (kg) 2500 3500 4500 5500

Probability 0.35 0.45 0.20 0.05

What was the expected weekly demand for wool based on the distribution?

an=-an-1+16an-2+4an-3-48an-4,where a°=0,a1=16,a2=-2,a3=142