Discrete Mathematics Answers

how propositional logic can be used in Boolean search? Give detail answer with an example of web page searching.

Q. Construct the truth tables for (p & q here are not above statement)

a) p V ~q
b) ~p V ~q
c) q -->p
d) ~(p-->q)-->r

Q 4: Find the Number of Mathematics students in a university taking at-least one of the language Mandarin, English and Japan Give the following data:

65 study Mandarin
45 study English
42 study Japanese
20 Study Mandarin and English
25 Study Mandarin an Japanese
8 study all three languages

There are 18 mathematics majors and 325 computer science majors at a college.
a) In how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major?
b) In how many ways can one representative be picked who is either a mathematics major or a computer science major?

Let A = {2,3,4} , B = {6,8,10} , and C = {a,b}
True or False?
(i) 4R6
(ii) 4R8
(iii) (3,8) ∈ R
(iv) (2,10) ∈ R
(v) (4,12) ∈ R

Show that A=B
A = {1,2,3}
B ={n|n∈Z+ and n^2<10}

Consider the statement: The art show was enjoyable but the room was hot.
a) Use a variable to represent each basic statement in the given statement.
b) Use the variables and logical operators to represent the statement in symbolic form.
c) Construct the truth table.

Define a function fm: N x N ->N as follows: fm(n, k) =k if 0 ≤ n < m, and fm(n, k) =fm(n-m, k+1) otherwise. Describe in terms of a single well-known arithmetic operation what fm(n, 0) is computing.

Write following using summation
n(n-1)+(n-2)++.....+1

Let A be a countable set, and B is another set. Assume further that there exists an onto function f:A->B. Is B necessarily countable? Provide a full justification for your answer.