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Number of relations on {1, 2, 3} containing (1, 2) and (2, 3) that are reflexive and transitive but not symmetric

The same question, asked 2 times: 12 Apr 2023, 22 Jan 2025. Every wording below, oldest first.

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  1. Question 1

    12 Apr 2023

    88
    The number of relations, on the set {1,2,3}\mathbf{\{ 1,2,3\}} containing (1,2)(1,2) and (2,3)(2,3), which are reflexive and transitive but not symmetric, is

  2. Question 2

    22 Jan 2025

    150
    Let A={1,2,3}\mathbf{A = \{ 1,2,3\}}. The number of relations on A , containing (1,2)(1,2) and (2,3)(2,3), which are reflexive and transitive but not symmetric, is  ____\ \_\_\_\_