1. Presentation V Computer Functioning By Teacher Julio Cesar Peñaloza Castañeda

2. 5.1 Basic Computer Functioning A computer can be defined as an electronic device that accepts data from an input device, processes it, stores it in a disk and finally displays it on an output device such as a monitor. The following figure illustrates how this flow of information exists for all types of computers such as Personal Computers, Laptops, Palmtops etc.

3. Flow of Information in a Computer

4. Tables of Truth Values

6. Example 1 Proposition: P: 31 is a prime number: Q: The ice is hot: Determine the value of truth of P, Q, P ^ Q, P ∨ Q

7. Solutions P = 1 (Because 31 IS a prime number) Q = 0 (It’s false that the ice is hot) P ^ Q = 0 (Because the when one of the propositions of a conjunction is false the conjunction is false) P ∨ Q = 1 (Because the when one of the propositions of a disjunction is true the disjunction is true)

8. Example 2 Proposition: P: There is life on the moon Q: 2 + 1 = 3 Determine the value of truth of P, Q, P ∨ Q, P^Q, P → Q, P↔Q

9. Solutions P=0 Q=1 P ∨ Q=1 P^Q=0 P → Q=1 P↔Q = 0

10. Example 3 Proposition: P: There are elephants in Mars Q: The Fire is cold R: 2+ 1 = 4 Symbolize and validate the following propositions: S: If there are elephants in Mars and the fire is cold, then 2 + 1 = 4 T: There are elephants in Mars and, fire IS cold so 2 + 1 = 4

11. Solutions S = (P ^ Q) → R = 1 T = P ^ (Q →R) = 0

12. Exercise 1 Make the table of truth values for the following proposition: T: (¬P^ Q) → (¬Q ∨ P) With the following values: 1. P=1, Q=1 2. P=1, Q=0 3. P=0, Q=1 4. P=0, Q=0

13. Exercise 2 If P, Q, R are truth and S, T, are false, determine the value of truth of the following propositions: 1. [P → (R → T)] ↔ [(¬P ^ S) → (Q → ¬T) 2. [(¬T ∨ ¬P) ↔ [ T →(R ∨ S)]] ↔[(P ^ Q ^ ¬T) →(¬Q → ¬S)]