Mathematical  Culture and Thought

Mathematical Culture and Thought

Symmetric Difference‎, ‎Cardinal‎, ‎and Probability

Document Type : Original

Authors
1 Department of Mathematics, Tafresh University, Iran
2 Department of Information Technology, Shahed University, Iran
Abstract
In the most mathematical texts‎, ‎there have been paid less attention to “symmetric difference” and its properties‎. ‎In this article‎, ‎after verifying some basic properties of this operation‎, ‎we provide a formula for computing the cardinal (res‎. ‎probability) of the sets (res‎. ‎events) obtained from the combination of symmetric difference of finite number of sets (res‎. ‎events)‎, ‎in terms of the cardinal (res‎. ‎probability) of the constituent sets (res‎. ‎events)‎. ‎Finally‎, ‎we end the article by an application in cryptography‎.
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[in Persian]

  • Receive Date 22 June 2022
  • Revise Date 27 November 2022
  • Accept Date 29 November 2022
  • Publish Date 22 June 2023