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Number of elements in a relation on pairs (a1, b1) R (a2, b2)

This type of question, asked 7 times: 10 Apr 2023, 11 Apr 2023, 15 Apr 2023, 9 Apr 2024, 24 Jan 2026 S1, 2 Apr 2026 S2, 5 Apr 2026 S2. All 7 questions below, oldest first.

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  1. Question 1

    10 Apr 2023

    155
    Let A={2,3,4}\mathbf{A = \{ 2,3,4\}} and B={8,9,12}\mathbf{B = \{ 8,9,12\}}. Then the number of elements in the relation
    R={((a1, b1),(a2, b2))∈(A×B,A×B):a1R =\left\{ \left( \left( a_{1},{\text{ }b}_{1} \right),\left( a_{2},{\text{ }b}_{2} \right) \right)\in (A \times B,A \times B):a_{1} \right.
    divides b2b_{2} and a2a_{2} divides  b1}\left. \ b_{1} \right\} is:

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  2. Question 2

    11 Apr 2023

    169
    Let A={1,3,4,6,9}\mathbf{A = \{ 1,3,4,6,9\}} and B={2,4,5,8,10}\mathbf{B = \{ 2,4,5,8,10\}}. Let RR be a relation defined on A×BA \times B such that R=R = {((a1,b1),(a2,b2)):a1≤b2\left\{ \left( \left( a_{1},b_{1} \right),\left( a_{2},b_{2} \right) \right):a_{1}\leq b_{2} \right. and  b1≤a2}\left. \ b_{1}\leq a_{2} \right\}. Then the number of elements in the set RR is

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  3. Question 3

    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:

  4. Question 4

    9 Apr 2024

    90
    Let A={2,3,6,7}\mathbf{A = \{ 2,3,6,7\}} and B={4,5,6,8}\mathbf{B = \{ 4,5,6,8\}}. Let RR be a relation defined on A×BA \times B by (a1,b1)R(a2,b2)\left( a_{1},b_{1} \right)R\left( a_{2},b_{2} \right) is and only if a1+a2=b1+b2a_{1}+a_{2}=b_{1}+b_{2}. Then the number of elements in RR is

  5. Question 5

    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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  6. Question 6

    2 Apr 2026 S2

    71
    Let A={2,3,4,5,6}A = \{ 2,3,4,5,6\}. Let R be a relation on the set A×AA \times A given by (x,y)R(z,w)(x,y)R(z,w) if and only if x divides z and y≤wy \leq w. Then the number of elements in RR is ____\_\_\_\_ .

  7. Question 7

    5 Apr 2026 S2

    71
    Let A={1,4,7}A = \{ 1,4,7\} and B={2,3,8}B = \{ 2,3,8\}. Then the number of elements, in the relation R={((a1, b1) R = \left\{ \left( \left( a_{1},{\text{ }b}_{1} \right) \right.\ \right.,  (a2, b2))∈((A×B)×(A×B)):a1+b2\left. \ \left( a_{2},{\text{ }b}_{2} \right) \right) \in ((A \times B) \times (A \times B)):a_{1} + b_{2} divides  a2+b1}\left. \ a_{2} + b_{1} \right\} is ____\_\_\_\_