MT131 Discrete Mathematics Assignment

Assignment Help Mathematics

Reference no: EM132736890

MT131 Discrete Mathematics - Arab Open University

Q-1: Without using truth tables, determine whether the proposition (p∧(p?q))?q is a tautology.
In the questions below suppose the variable x represents students and y represents courses, and: U(y): y is an upper-level course, M(y): y is a math course, F(x): x is a freshman, B(x): x is a full-time student. Write the statement using these predicates and any needed quantifiers.
All students are freshmen.
Every freshman is a full-time student.
No math course is upper-level.

Q¬-2:
Suppose that a,b,c∈Z. show that if a^2 |b and b^3 |c then a^6 |c.
Suppose that a∈Z. show that if a is odd then a^2+3a+5 is also odd.
Let a,b∈Z and n∈N. Show that if a≡b (mod n) and a≡c (mod n), then c≡b (mod n).

Q¬-3:
Suppose that A,B,C and D are sets. Prove that (A×B)∪(C×D)⊆(A∪C)×(B∪D).
Let B={2^n |n∈Z}. Show that the function f:Z→B defined as f(n)=2^n is bijective. Then find f^(-1).

Q¬-4:
This problem involves 8-digit binary strings such as 10011011 or 00001010.
How many such strings are there?
How many such strings end in 0?
How many such strings have 1's for their second and fourth digits?
How many such strings have 1's for their second or fourth digits?
Find how many 9-digit numbers can be made from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 if repetition is not allowed and all the odd digits occur first (on the left) followed by all the even digits.
How many permutations of the letters A, B, C, D, E, F, G are there in which the three letters ABC appear consecutively, in alphabetical order?

Q¬-5:
Two cards are dealt off a well-shuffled deck. You win $1 if the two cards are of different suits. Find the probability of your winning?
A coin is tossed 5 times. What is the probability that the first toss is a head or exactly 2 out of the five tosses are heads?
In a shuffled 52-card deck, what is the probability that neither the top nor the bottom card is a heart?
A bag contains 20 red marbles, 20 green marbles and 20 blue marbles. You reach in and grab 15 marbles. What is the probability that they are all the same colour?

Attachment:- Discrete Mathematics.rar

Reference no: EM132736890

Questions Cloud

What is the document that corporations should do : There is something that all corporations should make least annually to mitigate the risk. What is the document that corporations should do at least annually?

What amount of net sales would be shown on income statement : What amount of Net Sales would be shown on the income statement? Allowance for doubtful accounts300. Sales revenues57,200

Preparation for marketing the new scanner to customers : Describe the specific information you think will be helpful to the sales team in preparation for marketing the new scanner to customers.

What is maia alternative minimum taxable income : She itemized her deductions, deducting $8,130 in charitable contributions and $3,130 in state income taxes. What is Maia's alternative minimum taxable income?

MT131 Discrete Mathematics Assignment : MT131 Discrete Mathematics Assignment Help and Solution, Arab Open University - Assessment Writing Service - What is the probability that the first toss

How upper management can ensure a good fit : Decide how upper management can ensure a good fit between management and work context.

What should watch for if do such an evaluation : Is it a good idea to rate the performance of managers based solely on the DCF model, and what should you watch for if you do such an evaluation?

Prepare and submit a Statement of Financial Position : The Retained Earnings balance is a final calculation for the year. Prepare and submit a Statement of Financial Position (balance sheet) as at the end of year

What is the probability of default in the fourth year : What is the probability of default in the fourth year conditional on no earlier default given the cumulative probability of a company defaulting by years

User Account

All Pages