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Sets and Venn Diagrams Worksheet

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									                                           Sets and Venn Diagrams Worksheet

     1. Find n( A  B) for each pair of sets described.
           a) n(A) = 10, n(B) = 8, n( A  B) = 4
           b) n(A) = 7, n(B) = 12, A  B

     2. Find a formula for finding n( X  Y ) .

     3. For disjoint sets P and Q, give formulas for:
                a) n( P  Q)                          b) n( P  Q)

     4. If n( D  E )  n( D)  n( E ) how are sets D and E related?

     5. Given A = {1, 2, 3}, B = {2, 4, 6, 8} and C = {2, 3, 5, 7} find n ( A  B  C ) using the principle of
        inclusion and exclusion.

     6. For S, the set of letters in the word KEYBOARD
        A, the set of vowels in the word, and B, the set of letters in the word BOARD, list:

          a) A’               b) B’             c) A B               d) A B                       e) AB'
                                                                                                        '
          f) AB'
              '                         g) ( A  B)'                        h) ( A  B)'

     7. List all subsets of each:

          a) {green}                    b) {heads, tails}             c) {yes, no, maybe}

     8. Using your results from 7, predict the number of subsets of a set that contains 4 elements? Verify your
        prediction by listing all subsets of the set {2,4,6,8}.

     9. List the complement of each set A, for the given Universal set, S.

               a) S = the set of whole numbers less than 25
                  A = {2, 3, 5, 10, 15, 20}
               b) S = the set of letters in the alphabet
                  A = the set of consonants

     10. The Swiss embassy has 65 employees. Of these employees, 47 speak German, 35 Speak Italian, and
         20 speak both. How many speak neither language? Illustrate this situation with a Venn Diagram.

     11. Of 900 students at GPSS, 400 attend the first school dance of the year, and 550 attend the second
         school dance of the year. If 275 attended both dances, how many students at the school did not attend
         either dance?

Answers: 1a) 14 b) 12              3) a) n(P) + n(Q) b) 0            4) disjoint                    5) 8
        6) a) A’ = {K, Y, B, R, D} b) B’ = {K, E, Y} c) A B = {E, B, O, A, R, D}
d) A B = {O, A}            e) AB' = {K, E, Y, B, R, D}
                                 '                         f) AB' = {K, Y}
                                                                '                                   g)   ( A  B)' = {K, Y}
h) ( A  B)' = {K, E, Y, B, R, D}                  7) a) {green}, { } b) {heads}, {tails}, {heads, tails}, { }
8) 8    9) a) A’ = {0, 1, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24}   b) A’ = {A, E, I, O, U}     10) 3

								
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