Theoretical Foundations of Computer Science Question Bank

Replies

• 

  whiz.kid.aniket

  @AKD: add some more!:wink:
• 

  Ankita Katdare

  Please add more questions to this question bank. We can compile a PDF of those and keep it for download.
• 

  Ankita Katdare

  1. Prove the Distributive and De Morgan’s laws for logic.
  2. Give a direct proof for the following: Suppose x is an integer. Prove that if x is odd, then x+1 is
  even.
  3. Prove the following, using the proof by cases method: Suppose x is a real number, then -|x| ≤ x ≤
  |x|.
  4. Prove the following, using the proof by contradiction method. Suppose x and y are odd integers,
  then xy is odd.
  5. What, if anything, is wrong with the following proof:
  Suppose that m is an integer. Prove that if m
  2
  is odd, then m is odd.
  Proof:
  Assume m is odd. Then m = 2k+1 for some integer k. Therefore m
  2
  = (2k+1)
  2
  
  =4k
  2
  +4k+1 = 2(2k
  2
  +2k) +1, which is odd. Therefore if m
  2
  is odd, then m is odd.
  6. Given the premises s→(o∧r) and n∧¬o prove (using the rules of inference) the conclusion that ¬s.
  Be sure to label your steps and give the rules of inference you are using.
  7. Given the premise ∃x(p(x)∧q(x)) prove (using the rules of inference ) the conclusion that ∃x
  p(x)∧∃x q(x). Be sure to label your steps and give the rules of inference you are using.