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

**QUESTIONS**

- Define:

(i) premises (ii) contradiction (iii) tautology - 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

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 won’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