Discrete Mathematics Answers

∀x∃y(x + y = 2 ∧ 2x − y =1

6. Use truth tables to determine whether the argument form is valid. [5 Marks]
a. There is an undeclared variable or there is a syntax error in the first five lines.
b. If there is a syntax error in the first five lines, then there is a missing semicolon
c. There is not a missing semicolon

The generating function of the sequence {1,2,3...n..} is (1-z)².

Analyse the operations, using illustration, if two network shortest path algorithm, providing an example of each

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}