Does the Diophantine Equation 378x + 222y = 8

How many elements are in the set { 0, { { 0 } }?

Discrete Mathematics Basics
1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where ${\displaystyle (a,b)\in R}$ if and only if
I) everyone who has visited Web page a has also visited Web page b.
II) there are no common links found on both Web page a and Web page b.
III) there is at least one common link on Web page a and Web page b.

Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B.
a) the set of sophomores taking discrete mathematics in your school
b) the set of sophomores at your school who are not taking discrete mathematics
c) the set of students at your school who either are sophomores or are taking discrete mathematics
Use these symbols: ${\displaystyle \cap \cup }$

Use proof by Contradiction to prove that the sum of an irrational number and a rational number is irrational.

In a survey of X university students, 64 had taken Discrete mathematics course, 94 had taken Object Oriented Programming course, 58 had taken Digital Logic course, 28 had taken Discrete Mathematics and Digital Logic , 26 had taken Discrete Mathematics and Object Oriented Programming, 22 had taken Object Oriented Programming and Digital Logic course, and 14 had taken all the three courses. Find how many had taken one course only.

in DISCRETE MATHEMATICS & APPLICATIONS Write a note about application of mathematical induction in daily life. Give two examples (150 words).

Whats the type of the following function in discrete math&
${\displaystyle f:\{1,2,3,4..\}\to R}$
f(x) = 1/x