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Set Theory Test 32

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Set Theory Test 32
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  • Question 1
    1 / -0
    If A and B are any two sets, then A(AB)A\bigcup (A\bigcap B) is equal to 
    Solution

  • Question 2
    1 / -0
    Let U be set with number of elements in U is 2009.
    Consider the following statements : 
    I if A, B are subsets of U with n (AB)=280(A \cup B)= 280   then n(AB)=x13+x23=y13+y23n(A'\cap B')=x_{1}^{3}+x_{2}^{3}=y_{1}^{3}+y_{2}^{3}  for some positive integers x1,x2,y1,y2,x_{1},x_{2},y_{1},y_{2},  II If A is a subset of U with n (A) = 1681 and out of these 1681 elements, exactly 1075 elements below to a subset B of U, then n(AB)=m2+P1P2P3n(A-B)=m^{2}+P_{1}P_{2}P_{3}  for some positive integer m and distinct primes P1P2P_{1}P_{2}  Which of the statements given above is / are correct ?
    Solution

  • Question 3
    1 / -0

    Directions For Questions

    If A={1,2,5,7,9,10},B={3,4}A = \{1, 2, 5, 7, 9, 10\}, B = \{3, 4\} then

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    The number of subjections from AA to BB is
    Solution

  • Question 4
    1 / -0
    Given n(U)=20,n(A)=12,n(B)=9,n(AB)=4n(U) =20, n(A) =12, n(B) =9, n(A \cap B) =4, where U is the universal set, A and B are subset of U, then n((AB)C)=n((A \cup B)^C)=
    Solution

  • Question 5
    1 / -0
    If n(A)=115, n(B)=326, n(A-B)=47, then n(AB)n(A\cup B) is equal to
    Solution
    n(A)=115n(A)=115
    n(B)=326n(B)=326
    n(AB)=47n(A-B)=47
    \therefore   n(AB)=n(A)n(AB)n\left( A\cap B \right) =n\left( A \right) -n\left( A-B \right)
                            =11547=68=115-47=68
    \therefore   n(AB)=n(A)+n(B)n(AB)n\left( A\cup B \right) =n\left( A \right) +n\left( B \right) -n\left( A\cap B \right)
                             =115+32668=115+326-68
                             =326+47=326+47
                             =373=373
    Option A.
  • Question 6
    1 / -0
    X and Y are two sets and f:XYf:X\rightarrow Y. If f(c)={y;cX,yY}f(c)=\left\{ y;c\subset X,y\subset Y \right\} and f1(d)={x;dY,xX}{ f }^{ 1 }(d)=\left\{ x;d\subset Y,x\subset X \right\} , then the true statement is
  • Question 7
    1 / -0
    Let N= {1, 2, 3, ........., 10}, then sum of the product of number taken two at a time from the set N is 
    Solution

  • Question 8
    1 / -0
    The set (AB)(BC)(A\cap B')'\cup (B\cap C) is equal to?
    Solution
    (AB)(BC)\left( A\cap B' \right) '\cup \left( B\cap C \right)
    =(ABˉ)(BC)=\left( A\cap \bar B \right)\cup \left( B\cap C \right)
    =(AˉB)(BC)=\left( \bar A\cap B\right)\cup \left( B\cap C \right)
    =AˉBC=\bar A\cup B\cup C
    Hence, the answer is ABC. A'\cup B\cup C.
  • Question 9
    1 / -0
    if S is a set of p(x) is polynomial of degree <2 such that p(0)=, P(1)=1, p(x)>0 xε\forall \quad x\quad \varepsilon (0, 1) then 
    Solution

  • Question 10
    1 / -0
    The solution set of x2+5x+6=0x^{2}+5x+6=0 is ........
    Solution

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