Discrete Math Question Consider the relation R on Z defined by the rule that (a,b)

Let A, B, and C be sets. Show that ${\displaystyle (A-B)-C=(A-C)-(B-C)}$

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

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

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.

Complement of a Set: What do I do when a set contains an element that is not in the Universal Set
Let $U=\{x:x\in \mathbb{N},x>10andx<40\},A=5,10,20,40$.
The complement of the set should be
$A^c=\{\text{All natural numbers between greater than 10 and less than 40 except for 20}\}$ right?

Prove by mathematical induction: ${\displaystyle \mathrm{\forall }n\ge 1,1^3+2^3+3^3+\cdots +n^3=\frac{n^2{(n+1)}^2}{4}}$

Make fractions out of the following information, reduce, if possible,
1 foot is divided into 12 inches. Make a fraction of the distance from 0 to a-d
0 to a. = ___
0 to b. = ___
0 to c. = ___
0 to d. = ___