Identify the rule used in each of the following arguments: 

$$A1:\ \left(P\wedge Q\right)\ \rightarrow\ R$$  

$$A2:\ R\ \rightarrow\left(S\vee\ T\right)$$  

$$Conclusion:\ \left(P\ \wedge\ Q\right)\ \rightarrow\ \left(S\ \vee\ T\right)$$  

Identify the rule used in each of the following arguments:  

$$A1:\ \left[P\rightarrow\ \left(Q\ \wedge\ R\right)\right]$$  

$$A2:\ \left[R\oplus U\right]$$  

$$Conclusion:\ \ \left[P\rightarrow\ \left(Q\ \wedge\ R\right)\right]\ \wedge\ \left[R\ \oplus U\right]$$   

Identify the rule used in each of the following arguments: 

$$A1:\ \left[P\ \oplus\ Q\right]\ \rightarrow\ \left[R\ \wedge\ S\right]$$  

$$A2:\ \neg\left[R\ \wedge\ S\right]$$  

$$Conclusion:\ \neg\left[P\ \oplus\ Q\right]$$  

Identify the rule used in each of the following arguments: 

A1: If you are a worthy, then you can lift the hammer.

A2: You cannot lift the hammer.

Conclusion: You are not worthy.

Identify the rule used in each of the following arguments: 

A1: If you are a fan of Marvel, then you should watch Doctor Strange in the Multiverse of Madness.

A2: I am from Nueva Ecija.

Conclusion: If you are a fan of Marvel, then you should watch Doctor Strange in the Multiverse of Madness and I am from Nueva Ecija.

Identify the rule used in each of the following arguments:

A1: The number x is a prime number and is also even.

Conclusion: The number x is a prime number.

Identify all of the rules that are used in each of the following arguments:

$$A1:\ P\ \rightarrow\left(Q\ \vee\ R\right)$$  

$$A2:\ P$$  

$$A3:\ \neg R$$  

$$Conclusion:\ Q$$  

I. Modus Ponens

II. Addition

III. Simplification

IV. Conjunction

V. Modus Tollens

VI. Hypothetical Syllogism

VII. Disjunctive Syllogism

VIII. Resolution

Identify all of the rules that are used in each of the following arguments:

$$A1:\ P\ \wedge\ Q$$   

$$A2:\ P\rightarrow R$$  

  $$Conclusion:\ R$$  

I. Modus Ponens

II. Addition

III. Simplification

IV. Conjunction

V. Modus Tollens

VI. Hypothetical Syllogism

VII. Disjunctive Syllogism

VIII. Resolution

Identify all of the rules that are used in each of the following arguments:

$$A1:\ \left(P\ \rightarrow\ Q\right)\ \vee\ \left(R\ \rightarrow\ S\right)\$$    

  $$A2:\ \neg\left(P\ \rightarrow\ Q\right)\vee\ \left(W\right)$$  

$$A3:\ \neg W$$  

$$A4:\ \neg S$$  

$$Conclusion:\ \neg R$$  

I. Modus Ponens

II. Addition

III. Simplification

IV. Conjunction

V. Modus Tollens

VI. Hypothetical Syllogism

VII. Disjunctive Syllogism

VIII. Resolution

Identify all of the rules that are used in each of the following arguments:

   $$A1:\ You\ are\ a\ good\ person$$   

$$A2:\ You\ love\ your\ parents\ very\ much$$  

$$A3:\ If\ you\ are\ a\ good\ person\ and\ loves\ your\ parents\ very\ much,\ then\ you\ will\ have\ a\ happy\ life$$  

I. Modus Ponens

II. Addition

III. Simplification

IV. Conjunction

V. Modus Tollens

VI. Hypothetical Syllogism

VII. Disjunctive Syllogism

VIII. Resolution

Identify all of the rules that are used in each of the following arguments:

  $$A1:\ He\ likes\ Math\ and\ Science$$  

  $$A2:\ He\ is\ from\ Mars$$  

  $$A3:\ If\ he\ likes\ Math\ and\ is\ from\ Mars,\ then\ he\ is\ an\ alien$$  

   $$Conclusion:\ He\ is\ an\ alien.$$  

I. Modus Ponens

II. Addition

III. Simplification

IV. Conjunction

V. Modus Tollens

VI. Hypothetical Syllogism

VII. Disjunctive Syllogism

VIII. Resolution