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Number of reflexive and transitive but not symmetric relations containing given pairs

This type of question, asked 3 times: 12 Apr 2023, 22 Jan 2025, 7 Apr 2025. All 3 questions below, oldest first.

Try each one first, then open its answer.

  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  ____\ \_\_\_\_

  3. Question 3

    7 Apr 2025

    72
    The number of relations on the set A={1,2,3}A = \{ 1,2,3\} containing at most 6 elements including (1,2)(1,2), which are reflexive and transitive but not symmetric, is .