Functions-GATE Questions

Questions

  • 2

    At 23:00 , we say that f(EUF) = f(E) U f(F)

    raadjosePRO
    Reply

    Sir, when you give the example Wives(Indians U Software Engineer) = Wives(Indians) U Wives(Software Engineer) , dont we need to subtract the components where Wives(Indian Software engineer) as this will be repeated

    • raadjosePRO

      Also given that E and F are both subsets of A, there is bound to be common elements between them.

      Or do we ignore the duplicate items because it is a set, and duplicate items are not included in set.

    • getgatebook

      when A = {1,2,3} and B = {1,5,6} A U B = {1,2,3,5,6}. Here union operation automatically eliminates duplicates as that is the way set union is defined.

  • 1

    @18:43

    sabi7habi7
    Reply

    sir, you have given a counter example with an element 7. wat if 7 has a
    different image in C than all the elements in B

    • getgatebook

      If 7 is mapped to new element 11 then h is not on to right ? But in the question it is given that h is on to.
      One more point, some how if you find an arrangement such that h is on to and f and g both are on to then we can not say option D is correct. Think why ?

  • 1

    At 10:00 2nd gate problem

    sudiptasenpro
    Reply

    all n subsets X1, X2, … Xn are of size 3.
    So total number of elements in Xj in 3n.
    So ans = 3n
    is it correct? Summing up the no of elements in all Xj gives nothing but the count of repetitions of all the elements of S

    • getgatebook

      Yes, you are absolutely correct.

  • 2

    @19:06

    sagarsharmapro21
    Reply

    Hi Sir,
    f : A -> B
    E and F are subsets of A
    Considering following example
    A(Domain) = {1,2,3}
    B(images) = All subsets of A{{}{1}{2}{3}{1,2}{2,3}{1,3}{1,2,3}}
    As mentioned in the question E and F being subsets of A(Domain) – E {{1},{1,3},{2,3}} and F = {{2},{2,3}}

    If I take the below example instead of Indian and software engineer and if
    function is f(i) = i
    Then
    f(E U F) = f({{1},{1,3},{2,3}} U {{2},{2,3}}) = {{1},{1,3}{2}{2,3}}

    f(E ∩ F) = f({{1},{1,3},{2,3}} ∩ {{2},{2,3}}) = f({2,3})
    f({2,3}) = {2,3} This is same as following :

    f(E) = f({{1},{1,3},{2,3}}) = {{1},{1,3},{2,3}}
    f(F) = f({{2},{2,3}}) = {{2},{2,3}}
    f(E) ∩ f(F) = {2,3}.

    So Can you please help me out where am i going wrong?

    Then

    • sagarsharmapro21

      Ignore “Then” present at last in the comment – wrote it by mistake

    • getgatebook

      In one particular example if LHS and RHS are equal it doesn’t mean that they are equla in every case. There might be an example where LHS != RHS