Home / Math / Discrete Math / Sets And Relations Worksheets / Sets and Functions Worksheet

Sets and Functions Worksheet

Sets and Functions Worksheet
  • 1. If «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»U«/mi»«mo»=«/mo»«mo»{«/mo»«mn»1«/mn»«mo»,«/mo»«mn»2«/mn»«mo»,«/mo»«mn»3«/mn»«mo»,«/mo»«mn»4«/mn»«mo»,«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mn»10«/mn»«mo»}«/mo»«/math» the universal set for the sets  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»{«/mo»«mn»2«/mn»«mo»,«/mo»«mn»3«/mn»«mo»,«/mo»«mn»4«/mn»«mo»,«/mo»«mn»5«/mn»«mo»}«/mo»«/math» and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»=«/mo»«mo»{«/mo»«mn»1«/mn»«mo»,«/mo»«mn»2«/mn»«mo»,«/mo»«mn»3«/mn»«mo»,«/mo»«mn»4«/mn»«mo»,«/mo»«mn»5«/mn»«mo»,«/mo»«mn»6«/mn»«mo»}«/mo»«/math» , then verify that «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»A«/mi»«mo»§#8746;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§apos;«/mo»«mo»=«/mo»«mi»A«/mi»«mo»§apos;«/mo»«mo»§#8745;«/mo»«mi»B«/mi»«mo»§apos;«/mo»«/math»?
    1. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»A«/mi»«mo»§#8746;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§apos;«/mo»«mo»=«/mo»«mi»A«/mi»«mo»§apos;«/mo»«mo»§#8745;«/mo»«mi»B«/mi»«mo»§apos;«/mo»«/math»
    2. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»A«/mi»«mo»§#8746;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»=«/mo»«mi»A«/mi»«mo»§apos;«/mo»«mo»§#8745;«/mo»«mi»B«/mi»«mo»§apos;«/mo»«/math»
    3. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»A«/mi»«mo»§#8746;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§apos;«/mo»«mo»=«/mo»«mi»A«/mi»«mo»§apos;«/mo»«mo»§#8745;«/mo»«mi»B«/mi»«/math»
    4. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»A«/mi»«mo»§#8746;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§apos;«/mo»«mo»=«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»§apos;«/mo»«/math»
  • 2. If «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»U«/mi»«mo»=«/mo»«mo»{«/mo»«mi»a«/mi»«mo»,«/mo»«mi»e«/mi»«mo»,«/mo»«mi»i«/mi»«mo»,«/mo»«mi»o«/mi»«mo»,«/mo»«mi»u«/mi»«mo»}«/mo»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»A«/mi»«mo»=«/mo»«mo»{«/mo»«mi»a«/mi»«mo»,«/mo»«mi»e«/mi»«mo»,«/mo»«mi»i«/mi»«mo»}«/mo»«/math» and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»=«/mo»«mo»{«/mo»«mi»e«/mi»«mo»,«/mo»«mi»o«/mi»«mo»,«/mo»«mi»u«/mi»«mo»}«/mo»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»C«/mi»«mo»=«/mo»«mo»{«/mo»«mi»a«/mi»«mo»,«/mo»«mi»i«/mi»«mo»,«/mo»«mi»u«/mi»«mo»}«/mo»«/math» then: verify that «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#8745;«/mo»«mo»(«/mo»«mi»B«/mi»«mo»-«/mo»«mi»C«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»-«/mo»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»C«/mi»«mo»)«/mo»«/math»?
    1. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#8745;«/mo»«mo»(«/mo»«mi»B«/mi»«mo»-«/mo»«mi»C«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»+«/mo»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»C«/mi»«mo»)«/mo»«/math»
    2. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#8745;«/mo»«mo»(«/mo»«mi»B«/mi»«mo»-«/mo»«mi»C«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»-«/mo»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»C«/mi»«mo»)«/mo»«/math»
    3. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#8745;«/mo»«mo»(«/mo»«mi»B«/mi»«mo»+«/mo»«mi»C«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»-«/mo»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»C«/mi»«mo»)«/mo»«/math»
    4. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#8746;«/mo»«mo»(«/mo»«mi»B«/mi»«mo»-«/mo»«mi»C«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»-«/mo»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»C«/mi»«mo»)«/mo»«/math»

  • 3. Let «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»U«/mi»«mo»=«/mo»«mo»{«/mo»«mn»1«/mn»«mo»,«/mo»«mn»2«/mn»«mo»,«/mo»«mn»3«/mn»«mo»,«/mo»«mn»4«/mn»«mo»,«/mo»«mn»5«/mn»«mo»,«/mo»«mn»6«/mn»«mo»,«/mo»«mn»7«/mn»«mo»,«/mo»«mn»8«/mn»«mo»,«/mo»«mn»9«/mn»«mo»}«/mo»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»A«/mi»«mo»=«/mo»«mo»{«/mo»«mn»2«/mn»«mo»,«/mo»«mn»4«/mn»«mo»,«/mo»«mn»6«/mn»«mo»,«/mo»«mn»8«/mn»«mo»}«/mo»«/math» and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»=«/mo»«mo»{«/mo»«mn»2«/mn»«mo»,«/mo»«mn»3«/mn»«mo»,«/mo»«mn»5«/mn»«mo»,«/mo»«mn»7«/mn»«mo»}«/mo»«/math», verify that  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§apos;«/mo»«mo»=«/mo»«mi»A«/mi»«mo»§apos;«/mo»«mo»§#8745;«/mo»«mi»B«/mi»«mo»§apos;«/mo»«/math»?
    1. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§apos;«/mo»«mo»=«/mo»«mi»A«/mi»«mo»§apos;«/mo»«mo»§#8745;«/mo»«mi»B«/mi»«/math»
    2. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§apos;«/mo»«mo»=«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»§apos;«/mo»«/math»
    3. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§apos;«/mo»«mo»=«/mo»«mi»A«/mi»«mo»§apos;«/mo»«mo»§#8745;«/mo»«mi»B«/mi»«mo»§apos;«/mo»«/math»
    4. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»=«/mo»«mi»A«/mi»«mo»§apos;«/mo»«mo»§#8745;«/mo»«mi»B«/mi»«mo»§apos;«/mo»«/math»
  • 4. In a group of 40 students 26 take tea, 18 take coffee and 8 take neither of the two. How many take both tea and coffee?
    1. 11 students take both tea and coffee.
    2. 13 students take both tea and coffee.
    3. 10 students take both tea and coffee.
    4. 12 students take both tea and coffee.
  • 5.
    A and B are two sets such that:«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«mo»(«/mo»«mi»A«/mi»«mo»-«/mo»«mi»B«/mi»«mo»)«/mo»«mo»=«/mo»«mn»14«/mn»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mi»x«/mi»«mo»,«/mo»«mi»n«/mi»«mo»(«/mo»«mi»B«/mi»«mo»-«/mo»«mi»A«/mi»«mo»)«/mo»«mo»=«/mo»«mn»3«/mn»«mi»x«/mi»«/math» and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«mo»(«/mo»«mi»A«/mi»«mo»§#8745;«/mo»«mi»B«/mi»«mo»)«/mo»«mo»=«/mo»«mi»x«/mi»«/math» , draw a Venn diagram to illustrate information if and n(A) = n(B) then find the value of x?
    1.  x = 7
    2.  x = 5
    3.  x = -7
    4.  x = 6
  • 6. A survey of 500 television viewers produced the given information, 285 watch football, 195 watch hockey, 115 watch cricket, 45 watch football & cricket, 70 watch football & hockey, 50 watch cricket & hockey, 50 do not watch any of the three games. How many watch exactly one of the three games?
    1. 324
    2. 325
    3. 323
    4. 321
  • 7. There are 20 students in a Chemistry class and 30 students in a Physics class. Find the number of students which are either in Physics class or Chemistry class in the following cases:
    (i)      Two classes meet at the same time.
    (ii)    The two classes meet at different hours and ten students are enrolled in both the courses.
    1. (1) -50
      (2) 40
    2. (1) 50
      (2) -40
    3. (1) 50
      (2) 30
    4. (1) 50
      (2) 40
  • 8.  If «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»{«/mo»«mn»1«/mn»«mo»,«/mo»«mn»2«/mn»«mo»,«/mo»«mn»3«/mn»«mo»,«/mo»«mn»4«/mn»«mo»,«/mo»«mn»5«/mn»«mo»}«/mo»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»B«/mi»«mo»=«/mo»«mo»{«/mo»«mn»1«/mn»«mo»,«/mo»«mn»3«/mn»«mo»,«/mo»«mn»5«/mn»«mo»,«/mo»«mn»8«/mn»«mo»}«/mo»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»C«/mi»«mo»=«/mo»«mo»{«/mo»«mn»2«/mn»«mo»,«/mo»«mn»5«/mn»«mo»,«/mo»«mn»7«/mn»«mo»,«/mo»«mn»8«/mn»«mo»}«/mo»«/math» verify that «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»-«/mo»«mo»(«/mo»«mi»BuC«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»A«/mi»«mo»-«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§#8745;«/mo»«mo»(«/mo»«mi»A«/mi»«mo»-«/mo»«mi»C«/mi»«mo»)«/mo»«/math» ?
    1. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»-«/mo»«mo»(«/mo»«mi»BuC«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»A«/mi»«mo»-«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§#8745;«/mo»«mo»(«/mo»«mi»A«/mi»«mo»-«/mo»«mi»C«/mi»«mo»)«/mo»«/math»
    2. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»-«/mo»«mo»(«/mo»«mi»BuC«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»A«/mi»«mo»-«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§#8745;«/mo»«mo»(«/mo»«mi»A«/mi»«mo»+«/mo»«mi»C«/mi»«mo»)«/mo»«/math»
    3. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»-«/mo»«mo»(«/mo»«mi»BuC«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»A«/mi»«mo»+«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§#8745;«/mo»«mo»(«/mo»«mi»A«/mi»«mo»-«/mo»«mi»C«/mi»«mo»)«/mo»«/math»
    4. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»+«/mo»«mo»(«/mo»«mi»BuC«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»A«/mi»«mo»-«/mo»«mi»B«/mi»«mo»)«/mo»«mo»§#8745;«/mo»«mo»(«/mo»«mi»A«/mi»«mo»-«/mo»«mi»C«/mi»«mo»)«/mo»«/math»
  • 9. In a class of 35 students, 17 have taken Mathematics, 10 have taken Mathematics but not Economics. Find the number of students who have taken both Mathematics and Economics and the number of students who have taken Economics but not Mathematics, if it is given that each student has taken either Mathematics of Economics or both?
    1. (1) 7 students have taken both Mathematics and Economics.
      (2) 11 students have taken Economics but not Mathematics.
    2. (1) -7 students have taken both Mathematics and Economics.
      (2) 11 students have taken Economics but not Mathematics.
    3. (1) 7 students have taken both Mathematics and Economics.
      (2) -11 students have taken Economics but not Mathematics.
    4. (1) 7 students have taken both Mathematics and Economics.
      (2) 10 students have taken Economics but not Mathematics.
  • 10. In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H & I, II read both H & T, 8 read both T and I, 3 read all the three newspapers. Find:
    (i)      Number of people who read at least one of the newspapers.
    (ii)    Number of people who read exactly one newspaper.
    1. (1) 51 people read at least one of the newspapers.
      (2) 30 people read exactly one newspaper.

    2. (1) 52 people read at least one of the newspapers.
      (2) 31 people read exactly one newspaper.
    3. (1) 52 people read at least one of the newspapers.
      (2) 30 people read exactly one newspaper.
    4. (1) 42 people read at least one of the newspapers.
      (2) 30 people read exactly one newspaper.
Math Topics
    Facebook Facebook Facebook Share
Copyright 2008-2012. All Rights Reserved.