Consider the following clauses in a knowledge base:
A v ~B
~W v B
~A
W v B v M
Using this knowledge-base of clauses,
Show by a resolution-refutation proof that proposition M is
true.
Show by resolution inference and the direct proof method that
the proposition M is true.
Use the resolution method to decide if the following formulas
are valid or not. If the formula is valid, provide a resolution
proof; if it is not valid, provide an interpretation which
falsifies the formula.
(a) (A↔(A∧B))→(A→B)
Use boolean algebra to prove that:
(A^- *B*C^-) + (A^- *B*C) + (A* B^- *C) + (A*B* C^-) + (A*B*C)=
(A+B)*(B+C)
A^- is same as "not A"
please show steps to getting the left side to equal the right
side, use boolean algebra properties such as distributive,
absorption,etc
In general, what do you need to show to prove the following?:
(For example: to prove something is a group you'd show closure,
associative, identity, and invertibility)
a. Ring
b. Subring
c. Automorphism of rings
d. Ring homomorphism
e. Integral domain
f. Ideal
g. Irreducible
h. isomorphic
Prove the following statements!
1. If A and B are sets then
(a) |A ∪ B| = |A| + |B| − |A ∩ B| and
(b) |A × B| = |A||B|.
2. If the function f : A→B is
(a) injective then |A| ≤ |B|.
(b) surjective then |A| ≥ |B|.
3. For each part below, there is a function f : R→R that is
(a) injective and surjective.
(b) injective but not surjective.
(c) surjective but not injective.
(d)...
Use cardinality to show that between any two rational numbers
there is an irrational number. Hint: Given rational numbers a <
b, first show that [a, b] is uncountable. Now use a proof by
contradiction
(java) Show what the following program would print. Be sure to
show work space. (Hint: Watch out for integer division) SHOW
WORK
public class Q2{
public static void main(String[] args){
int a = 1, b = 4, c = 5;
double x = 3.0;
a = method (b,x);
System.out.println( "first: " + a + " " + b + " " + c);
a = 12;
b = 5;
c = method(a - b, 10.0) * 2;
System.out.println( "then: "...