education

# Define premises, contradiction, valid argument and tautology

``COURSE CODE:MTH 211COURSE TITLE:LOGIC AND LINEAR ALGEBRACLASS:ND2 CIVIL , MECHANICAL, ELECTRICAL AAND MECHANICALENGINEERING``

QUESTIONS

1. Define:
(i) premises (ii) contradiction (iii) tautology
2. hat is a valid argument, hence establish the validity of the premises. P1: Alll engineering student are intelligent. P2: Emmanuel is an engineering student

3) let  P: Mariam is an intelligent girl

Q: Mariam is able to provide solution to complicated problem.
S: Either mariam is an intelligent girl or she is not able to provide solution to the problem. Draw the truth table for S.
PREMISES : Premises are proposition affirmed as providing grounds or reasons for accepting the conclusion.

CONTRACTION (absurdity): A statement form that only false substitution instances is called contradiction. A statement or proposition that contradicts or denies another or itself and is logically incongruous.
Is a situation or ideas in operation to one another. A contradiction is a sentence together with its negation, and a theory is inconsistent if it include a contradiction OR a statement or proposition that contradict or denies another or itself and is logically incongruous.

TAUTOLOGY : Is a formular that is true in all possible state.
Tautology is a formular which is always true. It opposite is contradiction. Tautology can also be define as a logical statement in which the conclusion is equivalent to the premise.
Examples of tautology are;
Either it will rain tomorrow, or it wonâ€™t rain.
Bill will win the election, or he will not win the election.
She is brave, or she is not brave.

## 2) What is a valid argument, hence establish the validity of the premises

P1: Alll engineering student are intelligent.

P2: Emmanuel is an engineering student

[i]What is the valid argument? An argument is valid if the truth value of the premises logically guarantees the truth of the conclusion.

## [ii] Hence use the valid argument to establish the validity of the premises.

If p2: All engineering student are intelligent
P2: Emmanuel is an engineering student.
Therefore, Emmanuel is intelligent.
The answer is: EMMANUEL IS INTELLIGEENT