I’m working on a mathematics multi-part question and need an explanation and answer to help me learn.

PC type

Write down the laws in Theorem 7.1

Refer to Page 351 in the textbook
b) Use perfect induction to prove the absorption law: a(a+b)=a
Refer to pages 350 and 351 in the textbook for examples using proof by perfect induction

2) Let K be any Boolean algebra. A useful relation can be defined as the elements of K as follows:
x y (read as “x precedes y” ) if and only if xy=x.
a) If K is the Boolean Algebra of subsets of a set S, to what familiar relation on the subsets of S does
Correspond?
Refer to example 7.1 in page 348 in the textbook
b) Use the axioms and laws of Boolean algebra to prove the following properties of in an
arbitrary Boolean algebra K.
Make sure that when you use the axioms or laws, write that down in the proof
i) x x for all ∈ (Reflexive property)
ii) If x y and y x, then x=y (Antisymmetric property)
iii) If x y and y z, then x z (Transitive property)
3) Use Corollary 7.1 or 7.2 ( pages 358, 360) to determine whether (xy+x’y’)’ and x’y+xy’ are equivalent