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`Question: If every element which belongs to A also belongs to B and if every element which  belongs to B also belongs to A then the sets A and B are Answer:A: equalQuestion: Let A  1 2 3 4 and B  3 1 4 2 thenAnswer:A: ABQuestion: Let Ex  x23x   2  F21 and G 122 1 Which of the following statement is trueAnswer:A: EFGQuestion: A set which contains no elements is calledAnswer:A: a null set    Question: The symbol  denotes Answer:A: a void set    Question: Let A be the set of people in the world who are older than 200 years According  to  known statistics A isAnswer:A: a null set    Question: Let B  x  x 4 x is odd Then B is Answer:A: a null set    Question: Which statement is validAnswer:A: the  object of a set are sets themselvesQuestion: In any application of the theory of sets all the sets under investigation will likely  be  subsets of a fixed set We call this setAnswer:A: universe of discourse   Question: Mortgage payments areAnswer:A: annuity immediate  Question: The set of real numbers and its properties is called the Answer:A: real number systemQuestion: There is a natural way to pair off the points on the line and the real numbers  that is  each point will represent a unique real number and each real number will  be represented  by a unique point We refer to this line as theAnswer:A: real line  Question:   are not closed under the operation of divisionAnswer:A: Integers Question: The are those real numbers which can be expressed as the ratio of two integersAnswer:A: rational numbersQuestion: Examples of irrational numbers are Answer:A: sqrtpi sqrt2 sqrt3 Question: The real number a  is less than the real number b if Answer:A: b  a is a positive number  Question: Geometrically if a  b then the point a on the real line lies Answer:A: to the left of the point b    Question: Given A1  x 2  x  5  A2  x 2 leq x leq  5 A3  x 2  x leq 5  A4  x2 leq x   5 Which of the following statements is trueAnswer:A: A1 is an open interval  A2 is a closed interval A3 and A4 are open closed and  closed  openQuestion: Set of the form A  xx  1 B  x x  2   C  x x  3 are calledAnswer:A: infinite intervals     Question: Set A is bounded if there exists a positive number M such that Answer:A: xleq MQuestion: Let fArightarrow B which reads f is a function of A onto B The set A and B are called theAnswer:A: domain and codomain   Question: Let f assign to each real number its square that is for every real number x let fx  x2  The domain and co domain of f are Answer:A: both the real numbers   Question: If the domain and co domain of a function are both the same set then f is  frequently  calledAnswer:A: an operator or transformation on AQuestion: If f and g are functions defined on the same domain D and if f a  g a for every  ain D then the functions f and g are Answer:A: equalQuestion: Let f x  x2 where x is a real number Let gx  x2 where x is a complex number  Which of the following statements is trueAnswer:A: the function f is not equal to g since they have different domainsQuestion: Let f map A into B Then f is called a  if different elements in B are assigned to  different elements in AAnswer:A: injective functions   Question: are essentially a series or fixed payments required from you or paid to  you at  a specified frequency over the course of a fixed time periodAnswer:A: AnnuitiesQuestion: are primarily used as a means of securing a steady cash flow for an individual  during their retirement yearsAnswer:A: AnnuitiesQuestion: Straight bonds usually pay coupon payments at the end of every six months until  the bonds maturity date is an example of Answer:A: ordinary simple interest     Question: Payments that are required at the beginning of each period denotes Answer:A: annuity due Question: Let E  2 4 6   What is the compliment of the set EAnswer:odd numbersQuestion: The family of all the subsets of any set S is calledAnswer:the power set of SQuestion: Let S  a b c d and T  f b d g Then the intersection of set S and T isAnswer:b dQuestion: The sets A B Acap B and  B A are mutually disjoint impliesAnswer:the intersection of any two is the null setQuestion: The  are those real numbers which can be expressed as the ratio of two integersAnswer:rational numbersQuestion: Let M  ab Then 2M isAnswer:a b a b Question: Let P be the set of positive real numbers and let Q be the set of negative real numbers The union of P and Q consist of all the real numbers exceptAnswer:zeroQuestion: The real number a is less than the real number b if Answer:b  a is a positive numberQuestion:  is the set of elements which are common to A and B that is those elements which belong to A and which belong to BAnswer:The intersection of sets A and BQuestion: Let Px be any statement and let A be any set Then there exists a set Baain AP a is true The statement represents theAnswer:axiom of specificationQuestion: Let M  ab Then 2M isrnAnswer:D: a b a b Question: Let the function  fRightarrow R be defined by the formula fxx2   Then  f Answer:not a one one functionQuestion: Set A is bounded if there exists a positive number M such thatAnswer:xleq MQuestion: Let fxx2 where x is a real number Let gxx2 where x is a complex number Which of the statement is trueAnswer:the function f is not equal to g since they have different domainsQuestion: If f and g are functions defined on the same domain D and if f a  g a for every ain D then the functions f and g areAnswer:equalQuestion: Let the function  fRightarrow R be defined by the formula fxx2   Then the range of f consists of Answer:the positive real numbers and zeroQuestion: Let fAightarrow B  which reads f is a function of A onto B The set A and B are called theAnswer:domain and codomainQuestion: Let f assign to each real number its square that is for every real number x let fxx2 The domain and co domain of f areAnswer:both the real numbersQuestion: If the domain and co domain of a function are both the same set then f is frequently calledAnswer:an operator or transformation on AQuestion: Let f map A into B Then f is called a  if different elements in B are assigned to different elements in AAnswer:injective functionsQuestion: f fArightarrow B is if fa fa implies aa or equivalently aaimplies fafaAnswer:injective functionsQuestion: Let fArightarrow B  which reads f is a function of A onto B The set A and B are called theAnswer:domain and codomainQuestion: Let the function  fRrightarrow R be defined by the formula fxx2   Then  f Answer:not a one one functionQuestion: Let the function  fRrightarrow R be defined by the formula fxx2   Then the range of f consists of Answer:the positive real numbers and zero`