2. Express the following statements using quantifiers: a)There is a student who can speak Mandarin language. b)Some student has visited Australia but has not visited New Zealand...
2. Express the following statements using quantifiers: a)There is a student who can speak Mandarin language. b)Some student has visited Australia but has not visited New Zealand...
Consider the following compound propositions: A = (P→Q) Λ (Q→R) B = (P→R) a)Determine whether A ≡ B. Support your answer using truth table. Give reason for your...
number can be used once. examples. let say that the choosen numbers are 10, 11, 12, 15, 18, 25, 32, 36 you can write 11+25=36 or 10+12+18=15+25. i tried to prove for summation for...
There exists a set S such that the number of function f : S →{1,2,3} is 1000 true or false, please provide with explanation.
Using mathematical induction, prove that for any integer n, with n≥1, n(n2-1)(n+2) is divisible by 4.
A company conducts a survey every spring to measure the morale of its employees. A group to be surveyed is randomly selected from all employees who have been with the company for exactly 5 years....
Q: Suppose that you received the encrypted message 1074 2395 2208 1518 1074 2518 2400 2119 161 320 Decrypt the message using RSA Cipher with Key (2537,1949)
I have tried direct proof and proof by contradiction. Prove: 3(√2)-5 is irrational given that √2 is irrational Thats pretty much it, I have had a few starts but they dont go anywhere. &nb...
This is a problem that is supposed to use mathematical induction. I know how to create the basis case, and create the assumption using "k" but as soon as you are supposed to prove for...
There are 40 students in their first year of Computer Science program. All of these students must take either Discrete Math or Statistics, or both. There are 28 students in total taking Discrete Math...
Suppose a machine on average takes 108 seconds to execute a single algorithm step. What is the largest input size for which the machine will execute the algorithm in 2 seconds assuming the number...
Prove A is contained in B We know: A = {x I x=4s-1 for some s is an integer} B = {x I x=2t-1 for some t is an integer} Not even sure where to start,...
Prove that for every positive integer n, n ∑ k= 1, k2^k = (n-1)2n+1+2. I'm not really sure where to start with this problem, I think it may use mathematical induction....
Using the predicates P(x) to denote “x is a politician”, R(x) to denote “x is rich”, L(x) to denote “x is a lobbyist” and K(x, y) to denote “x knows y”, write down quantified logical stetements...
Suppose you are to prove the statement "The difference of any two odd integers is even." Re-write this statement as a universal conditional statement. What should the first sentence of a...
Show that the function f: N x N - > N x N, f(x,y) = (x+y, 2x-3y) is one-to-one. (A function f is said to be one -to -one , or injective , if and only if f ( a) = f ( b ) implies that...
Find all integer m such that 1848 Ξ 1914 (mod m) ? Explain.
Determine whether the function f: NxN --> Z with f(x,y) = (1-x^2)[y/3] is either: a) injective b) surjective Injective function A function...
Find the solution of recurrence relation an+1-an-1 = 2an for n ≥ 0 and satisfying initial conditions of a0=3 and a1=3.
a) Find inverse of 9 mod 1453, with Euclidean Algorithm. b) Solve linear congrunece : 9x+2 ≡ 6(mod 1453) using inverse of 9 mod 1453.