Prove using propositional calculus

Assignment Help Mathematics

Reference no: EM13832269

(1) Prove, using propositional calculus, that

~((PvQ)>R) <=> (P^~R)v(Q^~R)

(2) Given an example of a conjunction that is a tautology and a disjunction that is a contradiction

(3) Negate and put into positive form

a: (?x)[Q(x)>P(x)]

b: (∀x)(?y)(P(x)^Q(x))

c: (?x)(?y)(P(x)vQ(x,y))

d: [(?x)(~R(x))]v[(∀x)(Q(x)<>~P(x))]

(4) Let x and y be two integers. Prove that x^2+xy+y^2 is divisible by 9 if and only if x and y are divisible by 3. (Please provide the (=>) proof only, proof by contradiction)

Reference no: EM13832269

Questions Cloud

Evaluate integrals : Evaluate integrals : a) integral of [dz/(1 - z )^3 ] , C is circle |z| = 1/2 b) integral of [e^z/(1 - z )^3 ] dz , C is circle |z - 1| = 1/2

Applying the intermediate value theorem : Which of the properties below follow without further restriction on f by applying the Intermediate Value Theorem?A) f^2 (c) is 1/4 for some C in (-2,2)

An intersection of all remaining closed intervals : Consider the closed interval [0,1]. Remove the open interval 11 I which has center at 1/ 2and length 1/ 2 . 2 Then remove 12 I and 22 I from 11 I ? I so that their centers coincide with the center of closed interval of 11 [0,1]? I and their length 1/..

Choose the combining form which best completes : Choose the combining form which best completes

Prove using propositional calculus : (1) Prove, using propositional calculus, that ~((PvQ)>R) (P^~R)v(Q^~R) (2) Given an example of a conjunction that is a tautology and a disjunction that is a contradiction

Strengths and limitations of the two hr systems : What are the key strengths and limitations of the two HR systems in the context of the workplace and how do the two HR management systems relate to the accomplishment of strategic goals? What assumptions are you basing these views on?

Write blog posts entries based on given articles : In this assessment item, you are required to maintain an online reflective blog/journal and write blog posts/entries based on academic articles.

How did climate and food sources help shape native american : How did climate and food sources help shape Native American lifestyles

Family-owned business or a large multinational corporation : Whether it's a small family-owned business or a large multinational corporation, most businesses want to grow. There are many ways to grow a business in the short term, but there are fewer options for long-term sustainability.This week, you will begi..

User Account

All Pages