Logical Operator Replacement: b1 XOR b2 and deMorgan's Laws

  • Thread starter Thread starter courtrigrad
  • Start date Start date
  • Tags Tags
    Operator
Click For Summary

Homework Help Overview

The discussion revolves around the logical operator XOR (exclusive or) and its representation using deMorgan's Laws. Participants are exploring the equivalence of the expression b1 XOR b2 and its alternative forms in the context of mathematical logic and computer science.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the equivalence of b1 XOR b2 with various expressions, including the use of "not equal to" and deMorgan's Laws. Questions arise regarding the notation and terminology used in different fields, particularly between mathematical logic and computer science.

Discussion Status

The discussion is active, with participants providing insights and clarifications about the logical equivalences. There is recognition of differing terminologies and notations, but no explicit consensus has been reached on the preferred representation.

Contextual Notes

There is an indication that the context may be influenced by the field of computer science rather than pure mathematical logic, which could affect the interpretation of logical operators.

courtrigrad
Messages
1,236
Reaction score
2
Hello all

What can you replace b1 XOR b2 ? I tried using deMorgan's Laws. Is it b1 != b2 ?

thanks
 
Physics news on Phys.org
That certainly gives the same truth table, but I'm not familiar with != as a logical operator (I know it means "not equal to" in Comp Sci, but not in mathematical logic). I would think it would be:

~(b1=b2)

But maybe your book uses different notation. Anyway, you're right.
 
b1 XOR b2 is True in one of the two is true and the other false. It is False if they are both true or both false. It is equivalent to "((NOT b1) AND (b2)) OR ((b1) AND (NOT b2))" which is exactly the same as 'b1 NOT EQUAL b2".
 
this is for comp sci. not logic.

thanks
 
Well, there you go! :smile:
 

Similar threads

Ampere's Law and charge on the capacitor
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Pair of interacting systems, driven coupled harmonic oscillators
  • · Replies 7 ·
Replies
7
Views
3K
How Does Reversing Current Affect Magnetic Field Directions?
  • · Replies 7 ·
Replies
7
Views
2K
B-field at point P that is produced by the current in two wires
  • · Replies 2 ·
Replies
2
Views
3K
The factor by which the acoustic power is changed is 7943.28
  • · Replies 1 ·
Replies
1
Views
2K
Calculating Velocities in One-Dimensional Collisions
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad What is the difference between a complete basis and an overcomplete dictionary?
  • · Replies 5 ·
Replies
5
Views
3K
Magnetic Field due to a finitely long wire
  • · Replies 3 ·
Replies
3
Views
2K
Can Liquid Mercury Replace Copper in CVD Graphene Production?
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad What Are the Axioms of Fuzzy Logic and How Do They Extend Boolean Algebra?
  • · Replies 7 ·
Replies
7
Views
3K