What Is the Correct Truth Table for This Xor Equation?

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    Table Truth table
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Discussion Overview

The discussion revolves around the construction of a truth table for the expression (( X xor Y ) xor Z ) xor T, with a particular focus on the role and interpretation of the variable T. Participants explore whether T is consistently treated as a constant value of 1 (True) and the implications of this assumption on the truth table's correctness.

Discussion Character

  • Debate/contested, Technical explanation

Main Points Raised

  • One participant presents a truth table and assumes T is always 1, questioning its correctness.
  • Another participant challenges the assumption that T is always 1, asking for clarification on why this is the case and emphasizing the need for showing work in the solution.
  • Some participants agree that T can be interpreted as True, but there is ambiguity regarding whether T is simply a variable or a constant value.
  • A later reply humorously acknowledges a misunderstanding of T, suggesting it was initially thought to be a variable rather than a constant.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of T. While some accept T as always being True, others question this assumption and seek further clarification.

Contextual Notes

The discussion highlights the importance of defining variables clearly and the potential for misunderstanding in logical expressions. There is an unresolved question regarding the treatment of T and its implications for the truth table.

XodoX
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(( X xor Y ) xor Z ) xor T

I hope the truth table is correct. I'm not sure, because of the T. T is always 1, right?

X Y Z - (( X xor Y ) xor Z ) xor T

111 - 0
110 - 1
101 - 1
100 - 0
011 - 1
010 - 0
001 - 0
000 - 1
 
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I cannot fathom what T is or why you say it is always 1. Given the assumption that it is, then your solution is correct but you need to explain why T is always 1. You do not show it in your work.

And by the way, you are supposed to show your work, not just your final answer, else if you have something wrong how would we have any idea where you made a mistake?
 
T is always T (True), so: yes -- provided 1 is True in your 'system'.
I don't think I can improve on your table :wink:
 
BvU said:
T is always T (True), so: yes -- provided 1 is True in your 'system'.
I don't think I can improve on your table :wink:
Ah. "T" for "True". I thought it was just another variable. Good catch. It's early. I'm still asleep. That's my story and I'm sticking with it. :smile:
 

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