Logic:-

1. a) John is NOT an HCI major OR his starting salary is less than $40000 
   b) The instructor is NOT late AND Tom's watch is NOT slow
   c) Mary is NOT an IS major OR Mary's sister is NOT a CS major

2. a) P AND Q:  

      P  |  Q  |  P AND Q
      -------------------
      T  |  T   |    T
      T  |  F   |    F
      F  |  T   |    F
      F  |  F   |    F

   b) NOT P OR Q:

      P  |  Q  |  NOT P  |  NOT P OR Q
      --------------------------------
      T  |  T   |    F   |      T
      T  |  F   |    F   |      F
      F  |  T   |    T   |      T
      F  |  F   |    T   |      T

   c) (P OR Q) AND NOT (P AND Q):

      P  |  Q  | P OR Q | P AND Q | NOT(P AND Q) | (P OR Q) AND NOT (P AND Q)
      -----------------------------------------------------------------------
      T  |  T  |   T    |    T    |       F      |            F
      T  |  F  |   T    |    F    |       T      |            T
      F  |  T  |   T    |    F    |       T      |            T
      F  |  F  |   F    |    F    |       T      |            F


3. a) Tom: T; John: F; Mary: F
   b) Tom: T; John: T; Mary: F
   c) Tom: T; John: T; Mary: F
   d) Tom: T; John: F; Mary: T



Set Theory:-
 
   a) A UNION B = {20, 3, 5, 8, 17}
   b) A INTERSECTION B = {3, 5}
   c) A DIFFERENCE B = {20, 8}
   d) B DIFFERENCE A = {17}
   e) B PRODUCT C = {(3, 5), (3, 11), (5, 5), (5, 11), (17, 5), (17, 11)}
   f) B PRODUCT C PRODUCT D = {(3, 5, a), (3, 5, b),
                               (3, 11, a), (3, 11, b), 
                               (5, 5, a), (5, 5, b),
                               (5, 11, a), (5, 11, b),
                               (17, 5, a), (17, 5, b),   
                               (17, 11, a), (17, 11, b)}
   g) A INTERSECTION B UNION C = {3, 5, 11}