Logic 101 (#37): Killer Proof Strategy #1 (DeMorgan's Everything!)

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If you are stuck on a proof, try applying DeMorgan's rule wherever you can. It turns disjunctions into conjunctions, which can give you many simpler statements to work with.

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Thanks for these videos.

Here's mine:
1. ~(T v ~(P > Q)
2. Q > R
3. ~T ^ (P>Q) DeMorgan's:1
4. P>Q Simplification: 3
5. ~T Simplification: 3
6. P>R Hypothetical Syllogism: 4, 2
7. / (P>R) ^ ~T Conjunctive Syllogism: 6, 5

markp.

After a solid week of trying to find a reasonable way to solve the problem.

Thank you very much.

Anthony

fieldsofwickedness

You made that look so easy. Thank you, well explained.

without

i love you, a true life savior for a college student. will check out your other playlists and definitely subscribe

SpiritumTimoris

De Morgan, Simplification, Hypothetical Sillogism, Conjunction introduction, Conmutativity

lea

Mine solution:
1 | ~(T u ~(P => Q))
2 | Q => R | … (P => R) n ~T
3 | ~T n (P => Q) | 1 DeMorgan's law
4 | P => Q | 3 Simplification
5 | P => R | 2, 4 Hypothetical Syllogism
6 | ~T | 3 Simplification
7 | (P => R) n ~T | 5, 6 Conjunction Introduction

Double negation on line 3 is missing, I'll try not to forget next time. Thx for the videos btw.

no_name_

So...a Demorgan is basically chopping the formula in half, and if there is a negation before the brackets, add all the negation in properly to each letter like math?

lolunknown

Ok so here is my Proof:
((P=>Q)^(Q=>R))=>(P=>R)
this means, we can combine those premises 1 and 2 to the following:
~(Tv~(P=>R))
via de Morgan, we get:
~T^P=>R
since "^" is commutative, we get P=>R^~T q.e.d.

mariorpg

3 steps:
DeMorgan's Rule
Hypothetical Syllogism
Commutativity

poltergeist_gaming

Killer proof? More like "don't be aloof"...because there's no reason not to join in on the learning!

PunmasterSTP

Hi, are there more Logic 101 on the way?

TheLukeskywalker

Bit late, but this is my solution
1 ~(T v ~(P => Q))
2 Q => R
3 ~(T v ~(~P v Q)) 1 material implication
4 ~T ^ (~P ^ Q) 3 demorgan’s
5 (~T ^ ~P) ^ Q 4 associativity
6 (~P ^ ~T) ^ Q 5 communativity
7 ~P ^ (~T ^ Q) 6 associativity
8 ~P 7 simplification
9 Q 6 simplification
10 R 2, 9 modus ponens
11 ~T 4 simplification
12 ~P v R 8 disjunction introduction
13 P => R 12 material implication
14 (P => R) ^ ~T 13, 11 conjunction introduction

okxa

~(T v~(p => Q))
Q=> R

De Morgan’s law
(~T ^ (p => Q))
Commutative property
(p => Q) ^ ~T

spoonstraw

3. -(T v - (P=>R))
4. -((P=>R) v - T)
5. (P=>R) v T
6. (P=>R) ^ - T

shiroseki

Logic 101 (#37): Killer Proof Strategy #1 (DeMorgan's Everything!)

Logic 101 (#37): Killer Proof Strategy #1 (DeMorgan's Everything!)

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Logic 101 (#46): Proof By Cases (Killer Proof Strategy #3)

Logic 101 (#36): Introduction to Proofs

Logic 101 (#39): Proof By Contradiction/Indirect Proof

Logic 101 (#40): Conditional Proofs

Logic 101 (#16): Double Negation

Logic 101 (#31): Constructive Dilemma

Logic 101 (#43): Proof Practice #1

Logic 101 (#29): Disjunctive Syllogism

Logic 101 (#32): Destructive Dilemma

Logic 101 (#24): Hard Replacement Rule Problem

Logic 101 (#47): Biconditional Tautologies

Logic 101 (#30): Hypothetical Syllogism

Logic 101 (#19): DeMorgan's Law, Part 1

Logic 101 (#34.5): Biconditional Introduction and Elimination

Logic 101 (#35): Disjunction Introduction

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