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Problem Set 2

Module number: BEE3054

Problem 1. Either the princess or the queen attends the ceremony. The princess does not attend. Therefore, the queen attends. Formalize this statement taking care to define your variables. Construct a truth table for this argument and show the argument's validity using both natural deduction system and logic trees.

Problem 2. Construct a truth table for the following argument and show the argument's validity using both natural deduction system and logic trees.

P t Q,Q t R, -R H -P

Problem 3. Construct a truth table for the following argument and show the argument's validity using both natural deduction system and logic trees.

R H P 〜(P V (P A Q))

Problem 4. Construct a truth table for the following argument and show the argument's validity using both natural deduction system and logic trees.

H (—P A —Q) o —(P V Q)

Explain the connection between this argument and tautologies.

Problem 5. Using logic trees, either show that the following argument is valid or provide a counter-example.

P t (Q t R) H (P t Q) t R

Problem 6. Prove using natural deduction system and logic trees that

(—P) t P H P

Problem 7. Prove using natural deduction system and logic trees that

—(—P A —Q), —P H Q

Problem 8. Use the principle of mathematical induction to prove the following:

Theorem 1. For n > 1,

丈^k=2ⁿ⁽ⁿ+¹⁾

k=1