Search & Filtering
How many rows appear in a truth table for each of these compound propositions?
In a large region, there are 450 farmers. 250 pounds of farm beetroot, 110 pounds of farm yams, 75 pounds of farm radish, 45 pounds of farm beetroot and radish, 40 pounds of farm yams and radish, and 30 pounds of farm beetroot and yams Let B, Y, and R represent the farms that grow beets, yams, and radish, respectively.
Determine the number of farmers that farm beetroot, yams, and radish.
Directions: Read each statement carefully, show your complete solution if needed.
1. Write out all functions f: (1,2,3) – (a,b) (using two
- line notation). How many Function are there? How many are surjective? How many are bijective?
2. For each function give below. Determine whether or not the function in injective and whether or not the function is surjective.
(a) f: N – N given by f(n) = n + 4
(b) f: Z – Z given by f(n) = n + 4
(c) f: Z – Z given by f(n) = 5n – 8
Quantify the following propositions
1. Not all Russian agree with Putin.
2. Nobody is perfect.
3. There is some bad news about Ukraine that every student heard.
4. Either every Russian is proud, or every Russian is guilty.
5. Ukranian soldiers don’t give up.
6. No student likes any exams.
7. Hyun-bin has a cat.
8. All students will pass the exam.
9. Some students will pass all the exams.
10. Everybody is looking forward to summer vacation.
.Let A = {1, 2, 3, 4, 5} and B = {0, 3, 6}. Find a) A ∪ B. b) A ∩ B. c) A − B. d) B − A
Translate these statements into English, where C(x) is “x is a comedian” and F(x) is “x is funny” and the domain consists of all people.
a) ∀x(C(x) → F(x))
b) ∀x(C(x) ∧ F(x))
c) ∃x(C(x) → F(x))
d) ∃x(C(x) ∧ F(x))
Five thousand lottery tickets are sold for $1 each. One ticket will win $1000, two tickets will win $500 each, and ten tickets will win $100 each. Let X denote the net gain from the purchase of a randomly selected ticket.
a. Construct the probability distribution of C
b. Compute the standard deviation of X
a.{x|x is a real number such that x²=2}
b. {x|x is a positive integer less than 10}
c.{x|x is the square of an integers and x<10}
d. {x|x is an integer such that x²=3}
Determine whether an Ex-OR or OR is needed for following propositions:
i. Coffee or tea comes with dinner.
ii. Experience with C++ or java is required.
iii. Lunch includes soup or salad.
Prove that ((𝑝 → 𝑞) ⋀ ¬𝑞 ) → ¬𝑝 ) it’s tautology without using truth table?
