Logica

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).
5. Write down your opinion about this home work

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.

ANSWERS
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...