. How many 3 permutations are there on the set { 1, 2, 3, 4, 6 }

.  How many 3 permutations are there on the set  { 1, 2, 3, 4, 6 }   



2.   How many 4 sequences are there on the { 1, 2, ….. 8 }  that start with 2?

3.  How many menus are possible choosing 1 of 4 entrees, 2 of 3 appetizers, and 2 of 5 desserts?


4. Complete the truth table                                      
  P    Q     ~ P      P ∨ Q      ~ P ∧  ( P ∨ Q )                     
  T    T
  T    F
  F    T
  F    F

5. Prove by direct proof that the sum of two odd numbers “x” and “y” is even.


6.  Of the 20 students that took the quiz,
      12 got question 2 correct, 8 got question
      3 correct, and 5 got both correct. How many 
       got neither correct?



7.  50 people took a survey. 27 said they liked football, 22 liked baseball. 23 liked soccer, 10 liked football and baseball, 6 liked baseball and soccer, 11 liked football and soccer, and 4 liked all three. How many like baseball, but not football?  ( Use a Venn diagram to solve )

8.   For problems # 11 – 12,   Let   A = { 0, 2, 4, 8 }          B =  { 1, 2, 3, 4, 5 }            C =  { 1, 3, 5, 7, 9 }
11.       A ∪ B  =   ?                                                                     12.   ( A 


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