Understanding Logical Equivalencies in ~p ^ q and F: Explained Simply

  • Thread starter Thread starter mohabitar
  • Start date Start date
Click For Summary

Homework Help Overview

The discussion revolves around logical equivalencies, specifically focusing on the expression ~p ^ q and its relationship to the constant false (F). Participants are trying to clarify the reasoning behind substitutions and the implications of using F in logical expressions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the substitution of F for ~p ^ q and questioning the implications of this substitution. There is a focus on understanding how false interacts with other logical expressions, particularly in terms of equivalency.

Discussion Status

The discussion is active, with participants seeking to clarify their understanding of logical operations involving false. Some have offered insights into the nature of false in logical expressions, while others are still grappling with the implications of these substitutions.

Contextual Notes

There appears to be some confusion regarding the representation of false (F) and its role in logical equivalencies, as well as the notation used for true (T). Participants are questioning the assumptions behind these representations and their application in the context of the problem.

mohabitar
Messages
140
Reaction score
0
kdYpm.png


Everything in here makes sense up and till the last part, where they substituted (I think) F in for ~p ^ q, and then just ignored it and made it equivalent to the last part? Hope I'm not being too vague here.
 
Physics news on Phys.org
They observed that ((not p) and p) is always false (F). Then they used that (false or anything)=anything. Is it the 'F' that throwing you off?
 
Oh ok I see so false and anything is always anything. That makes sense. So the F represents a substitution of the previous part but is also used to symbolize false, correct?
 
mohabitar said:
Oh ok I see so false and anything is always anything. That makes sense. So the F represents a substitution of the previous part but is also used to symbolize false, correct?

F=false. Presumably they would write T=true. And (false and anything)=false, that's not what they used. (false or anything)=anything.
 

Similar threads

Logic: proof that [p -> (q ^ r)] <=> [(p ^ -q) -> r]
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Translate compound proposition p → q (implication) to p↓q question
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?
  • · Replies 9 ·
Replies
9
Views
3K
How Do Logic and Truth Tables Enhance Understanding in Algebra?
  • · Replies 5 ·
Replies
5
Views
3K
How to Interpret the Basic Logic Problem with Predicate P(x,y,z)
  • · Replies 2 ·
Replies
2
Views
2K
Possible Results and Probabilities of a Measurement of Operator Q
  • · Replies 7 ·
Replies
7
Views
3K
GF(q); x^p-x+a has no root => irreducible [PROOF]
  • · Replies 6 ·
Replies
6
Views
3K
Understanding the solution to a calculus problem (removable discontinuities)
  • · Replies 2 ·
Replies
2
Views
2K
Is It is not Monday and it is not Tuesday Equivalent to ~(P v Q)?
  • · Replies 2 ·
Replies
2
Views
2K
Show a certain sequence in Q, with p-adict metric is cauchy
  • · Replies 5 ·
Replies
5
Views
2K