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Assignment 1
Deadline: March 23

   Harshit Kumar

   March 16, 2012
Use Truth Table to prove the following

1. P → Q = ¬P ∨ Q
2. P ←→= (P → Q) ∧ (Q → P )
3. Distributive Law

   (a) P ∧ (Q ∨ R) = (P ∧ Q) ∨ (P ∧ R)
   (b) P ∨ (Q ∧ R) = (P ∨ Q) ∧ (P ∨ R)
4. DeMorgan’s Law
   (a) ¬(P ∨ Q) = ¬P ∧ ¬Q
   (b) ¬(P ∧ Q) = ¬P ∨ ¬Q
5. Idempotent Law
   (a) P ∨ (P ∧ Q) = P
   (b) P ∧ (P ∨ Q) = P

For Q5, Provide all three methods of proof, as discussed in the class.




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Dm assignment1

  • 1. Assignment 1 Deadline: March 23 Harshit Kumar March 16, 2012
  • 2. Use Truth Table to prove the following 1. P → Q = ¬P ∨ Q 2. P ←→= (P → Q) ∧ (Q → P ) 3. Distributive Law (a) P ∧ (Q ∨ R) = (P ∧ Q) ∨ (P ∧ R) (b) P ∨ (Q ∧ R) = (P ∨ Q) ∧ (P ∨ R) 4. DeMorgan’s Law (a) ¬(P ∨ Q) = ¬P ∧ ¬Q (b) ¬(P ∧ Q) = ¬P ∨ ¬Q 5. Idempotent Law (a) P ∨ (P ∧ Q) = P (b) P ∧ (P ∨ Q) = P For Q5, Provide all three methods of proof, as discussed in the class. 1