What Is the Correct Truth Table for This Xor Equation?

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SUMMARY

The discussion centers on the truth table for the expression ((X xor Y) xor Z) xor T, where T is defined as always being True (1). Participants confirm that the truth table provided is correct under the assumption that T is consistently True. The truth values for the combinations of X, Y, and Z are analyzed, leading to a consensus that the interpretation of T as True is crucial for the accuracy of the truth table.

PREREQUISITES
  • Understanding of logical operators, specifically XOR (exclusive OR).
  • Familiarity with truth tables and their construction.
  • Basic knowledge of Boolean algebra.
  • Experience with logical expressions in programming or mathematical contexts.
NEXT STEPS
  • Study the properties of XOR operations in Boolean algebra.
  • Learn how to construct truth tables for complex logical expressions.
  • Explore the implications of using constants like True (1) in logical equations.
  • Investigate how logical expressions are evaluated in programming languages such as Python or Java.
USEFUL FOR

This discussion is beneficial for students of computer science, mathematicians, and software developers who are working with logical expressions and truth tables in their projects or studies.

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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