Logic:

1. Write negations for each of the following:

   a) John is an HCI major AND his starting salary is at least $40000 
   b) The instructor is late OR Tom's watch is slow
   c) Mary is an IS major AND Mary's sister is a CS major

2. Let P and Q represent propositions. Construct truth tables for each of the 
   following compound propositions:

   a) P AND Q
   b) NOT P OR Q
   c) (P OR Q) AND NOT (P AND Q)

3. Tom, John and Mary are DePaul CTI students. Tom is an undergraduate student
   majoring in HCI. He is 26 years of age. John is a graduate student and is 
   also majoring in HCI. He is 36 years of age. Mary is also a graduate student  
   but is majoring in DS. She is 24 years of age. 

   Let P, Q, R represent the following propositions:

   P: Age > 25
   Q: Major is HCI
   R: Standing is undergraduate

   Given these propositions consider the following compound propositions. Examine
   the facts for Tom, John, and Mary presented above and, in each case, determine 
   the truth value of each compound proposition.
 
   a) P AND Q AND R 
   b) P AND Q OR R
   c) P OR NOT Q AND R
   d) NOT P AND NOT Q OR R


Set Theory:

Consider the following sets:

   A = {20, 3 , 5 , 8}
   B = {3, 5, 17}
   C = {5, 11}
   D = {a, b}

Determine the set which results in each case below:

   a) A UNION B
   b) A INTERSECTION B
   c) A DIFFERENCE B
   d) B DIFFERENCE A
   e) B PRODUCT C
   f) B PRODUCT C PRODUCT D
   g) A INTERSECTION B UNION C