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Decide if a relation on ordered pairs is reflexive, symmetric or transitive

This type of question, asked 6 times: 31 Jan 2023, 29 Jan 2024, 1 Feb 2024, 4 Apr 2024, 8 Apr 2024, 23 Jan 2025. All 6 questions below, oldest first.

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  1. Question 1

    31 Jan 2023

    74
    Let RR be a relation on N×NN \times N defined by (a,b)R(c,d)(a,b)R(c,d) if and only if ad(b−c)=bc(a−d)ad(b - c) = bc(a - d). Then RR is

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  2. Question 2

    29 Jan 2024

    77
    Let RR be a relation on Z×ZZ \times Z defined by (a,b)R(c,d)(a,b)R(c,d) if and only if ad - bc is divisible by 5 . Then RR is

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  3. Question 3

    1 Feb 2024

    164
    Consider the relations R1R_{1} and R2R_{2} defined as aR1baR_{1}b ⇔a2+b2=1\Leftrightarrow a^{2}+b^{2}= 1 for all a,b,∈Ra,b, \in R and (a,b)R2(c,d)(a,b)R_{2}(c,d) ⇔a+d=b+c\Leftrightarrow a + d = b + c for all (a,b),(c,d)∈N×N(a,b),(c,d) \in N \times N. Then

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  4. Question 4

    4 Apr 2024

    154
    Let a relation RR on N×NN \times N be defined as: (x1,y1)R(x2,y2)\left( x_{1},y_{1} \right)R\left( x_{2},y_{2} \right) if and only if x1≤x2x_{1}\leq x_{2} or y1≤y2y_{1}\leq y_{2} Consider the two statements: (I) RR is reflexive but not symmetric. (II) RR is transitive Then which one of the following is true?

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  5. Question 5

    8 Apr 2024

    168
    Let A={2,3,6,8,9,11}\mathbf{A = \{ 2,3,6,8,9,11\}} and B={1,4,5,10,15}\mathbf{B = \{ 1,4,5,10,15\}} Let RR be a relation on A×BA \times B define by (a,b)R(c,d)(a,b)R(c,d) if and only if 3ad−7bc3ad - 7bc is an even integer. Then the relation RR is

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  6. Question 6

    23 Jan 2025

    139
    Let X=R×RX = R \times R. Define a relation R on X as:
    (a1,b1)R(a2,b2)⇔b1=b2.\left( a_{1},b_{1} \right)R\left( a_{2},b_{2} \right)\Leftrightarrow b_{1}=b_{2}.
    Statement-I: R is an equivalence relation. Statement-II: For some (a,b)∈X(a,b) \in X, the set S={(x,y)∈X:(x,y)R(a,b)}\mathbf{S = \{(x,y) \in X:(x,y)R(a,b)\}} represents a line parallel to y=xy = x. In the light of the above statements, choose the correct answer from the options given below:

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