LOGIC PROOF QUESTION MODULE 5 RULES YOU CAN USE 1 modus pon

LOGIC PROOF QUESTION

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MODULE 5 RULES YOU CAN USE:

1) modus ponens (MP): the rule of logic stating that if a conditional statement (“if p then q ”) is accepted, and the antecedent ( p ) holds, then the consequent ( q ) may be inferred.

2) modus tollens (MT): the rule of logic stating that if a conditional statement (“if p then q ”) is accepted, and the consequent does not hold ( not-q ), then the negation of the antecedent ( not-p ) can be inferred.

3) pure hypothetical syllogism (HS): The form of hypothetical syllogism is: “If P, then Q. If Q, then R. Therefore, if P, then R.”

4) disjunctive syllogism (DS): In classical logic, disjunctive syllogism(historically known as modus tollendo ponens) is a valid argument form which is a syllogism having a disjunctivestatement for one of its premises. Either the breach is a safety violation, or it is not subject to fines.

Please do the proof with only the above 4 rules, if you would indicate which rules used it would also be helpful, thank you.

Problem 2.2 Consider the facts stated below. Answer the question that follows the facts. In doing this, you need to use your propositional reasoning skills. Using PL, construct a symbolic model of the logical structure of your argument. Using only the inference rules from Module 5, construct a proof of your argument *PL Propositional Logic Facts If we are going to have students use the computer lab on Friday then the lab needs to be ready by Thursday evening. If the lab needs to be ready by Thursday evening then all of the new computers must be received by Tuesday It turns out that all of the new computers were not received by Tuesday All of the new computers were received by Wednesday If all of the new computers were received by Wednesday and we cannot have students use the computer lab on Friday then we will have the students use the computer lab on Monday Question: When will we have the students use the computer lab? Note: the answer to this question is your conclusion. The premises for your reasoning process are the facts given above.)

Solution

From the above facts which are mentioned

let us assume

P: Students use the computer lab on friday

Q : Lab needs to be ready by thursday evening

R: New computers to be received by tuesday

From these statements according to Rule 3-->

\"IF R then Q, IF Q then P\"

If the new computers received on wednesday. Then this rule will not be satisfied.

From Rule 2 : if ~R then ~Q

: if ~Q then ~P

Hence if computers received on wednesday students use the lab on monday.