A Find the argument form for the following argument and dete

A. Find the argument form for the following argument and determine whether it is valid.

If I graduate this semester, then I will have passed the CSC1500 course.

If I do not study CSC1500 for 10hours a week, then I will not pass CSC1500.

If I study CSC1500 for 10hours a week, then I cannot play tennis.

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If I play tennis, I will not graduate this semester.

B. Use the rules of Boolean arithmetic to find an expression using fewer operations that are equivalent to expression

found in Part A. Give the truth table and draw a logic diagram for this expression.

Solution

A -> graduate this semester
B -> passed the CSC1500
C -> study CSC1500 for 10 hours a week
D -> play tennis

Statement 1: If I graduate this semester, then I will have passed the CSC1500 course.

   A -> B

Statement 2: If I do not study CSC1500 for 10hours a week, then I will not pass CSC1500.

   !C -> !B

Statement 3: If I study CSC1500 for 10hours a week, then I cannot play tennis.
  
   C -> !D

To Check : If I play tennis, I will not graduate this semester.
Therefore, D is true and A is false

Now we have
   (A -> B) ^ (!C -> !B) ^ (C -> !D)
   (!A V B) ^ (C V !B) ^ (!C V !D)
   (T) ^ (C V !B) ^ (!C)
   (C V !B) ^ (!C)

   so, if !C will true the whole argument will true

A |   D |   C |   B
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F T T T/F = F
F T F F        = T