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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.
ANSWERS
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.



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

Oluwamuyide Peter

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