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Number of elements in the relation (a, b) R (c, d) iff 2a + 3b = pc + qd on {1, 2, 3, 4} x {1, 2, 3, 4}

The same question, asked 2 times: 15 Apr 2023*, 24 Jan 2026 S1. Every wording below, oldest first.

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  1. Question 1

    15 Apr 2023

    85
    Let A={1,2,3,4}\mathbf{A = \{ 1,2,3,4\}} and RR be a relation on the set A×AA \times A defined by R={((a,b),(c,d)):2a+3b=4c+5d}\mathbf{R = \{((a,b),(c,d)):2a + 3b = 4c + 5d\}}. Then the number of elements in RR is:

  2. Question 2

    24 Jan 2026 S1

    62
    Let R be a relation defined on the set {1,2,3,4}×{1,2,3,4}\mathbf{\{ 1,2,3,4\} \times \{ 1,2,3,4\}} by R={((a,b),(c,d)):2a+3b=3c+4d}\mathbf{R = \{((a,b),(c,d)):2a + 3b = 3c + 4d\}}. Then the number of elements in R is

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