# Logica

Páginas: 4 (897 palabras) Publicado: 6 de marzo de 2011
LOGIC

Write down the following home work in English:

1. What is a statement (proposition)? (Write down examples).
2. What is a logic connective? (Write down examples).
3. What is atautology? (Write down examples)
4. Explain what is the difference between implication and conditional? (Write down examples).

Remark:
The homework must begiven to the teacher on 17th, 18th, 19th of February by written
You can do the homework in group of three students.

1. A proposition or statement is a sentence that can be false or truebut not both simultaneously; the proposition is a fundamental element of the mathematical logic. Is a declarative statement that is represented by propositional variables symbolized by small letterslike p, q, r, s, t, etc.
There are simple (atomic), compound (molecular), open or close propositions.
Examples:
a. The Earth is flat. (This is a simple (atomic) proposition)
b. 5 is a even numberor 5 is a odd number. (This is a compound (molecular) proposition)
c. 2x-1=3 (Px: 2x-1=3). (This is a open proposition)
d. 2x-1=3 is valid for x=1 (Px: 2x-1=3). (This is a close proposition)
2. Alogic connective is a symbol or word used to connect two or more propositions, used to attach the propositions p, q and obtain a compound proposition; joining two atomic propositions to form amolecular proposition.
The logical connectives are negation (not)(¬ or ~), conjunction (and)( or &), disjunction (or)( ), conditional (if…then)( , or ) and biconditional (if and only if)( ).Examples:
For statement P = It is raining and Q = I am indoors.
It is not raining (¬P)
It is raining and I am indoors (P Q)
It is raining or I am indoors (Q P)
If it is raining, then I am indoors (PQ)
It is raining if and only if I am indoors (P Q)

3. A tautology is a proposition whose truth table always gives the truth value (V) in all possible cases of true values (V, F) of each of...

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