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Let R and S be two non - void relations ...

Let R and S be two non - void relations on a set A.

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A `to` (s) B `to`( r ) C `to` ( P ) D `to` ( q )
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Let R and S be two relations on a set A. If (ii) R is reflexive and S is any relation prove that R cup S is reflexive

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Knowledge Check

  • Let f:XtoY and A,B are non-void subsets of Y, then

    A
    `f^(-1)(A)-f^(-1)(B)supsetf^(-1)(A-B)` but the opposite does not hold
    B
    `f^(-1)(A)-f^(-1)(B)subsetf^(-1)(A-B)` but the opposite does not hold
    C
    `f^(-1)(A-B)=f^(-1)(A)-f^(-1)(B)`
    D
    `f^(-1)(A-B)=f^(-1)(A)cupf^(-1)(B)`

  • Let R = {(1,3),(2,2),(3,2)} and S = {(2,1),(3,2),(2,3)} be two relations on set A = {1,2,3}. Then R o R is equal

    A
    {(2,3),(3,2),(2,2)}
    B
    {(1,3),(2,2),(3,2),(2,1),(2,3)}
    C
    {(3,2),(1,3)}
    D
    {(2,3),(3,2)}

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    Let R be an equivalence relation on a finite set A having n elements. Then the number of ordered pairs in R is

    Let R be the relation defined on the set of natural numbers NN by, (x,y) in R rArr2x+3y=20and x,y in NN Find R and R^-1 , the inverse relation of R, as sets of ordered pairs.

    Let S and T be two non- empty sets. Show that, f:SxxT rarr TxxS defined by , f(a,b)=(b,a) for all (a,b) in Sxx T is a bijection.

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