What is the name of the following format of logical argument?

If A, then B.

Not A.

Therefore not B.

What is the name of the following format of logical argument?

If A, then B.

If B, then C

Therefore, if A then C.

P1: If I am happy, then I smile.

P2: I am not smiling.

C: Therefore I am not happy.

P1: If you go get gas, then you can drive your car.

P2: You cannot drive your car.

C: Therefore, you cannot go get gas.

P1: If you're sick, then you must stay home.

P2: You're sick.

C: Therefore, you must stay home.

P1: If Eagles are birds, then Eagles fly.

P2: Eagles are birds.

C: Therefore, eagles fly

If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Conditional: If x = 2, then 2x – 10 = –6.

Premise: x = 2

If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Conditional: If two lines do not intersect, then they are coplanar and parallel, or skew.

Premise: Lines AB and CD do not intersect.

If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Conditional: If points lie on a line, then they are collinear.

Premise: Points X, Y, and Z are in line m.

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Conditional: If Jack goes to school, then it is Monday.

Premise: Jack doesn't go to school.

If I comb my hair, then I won't have tangles.

I have tangles.

Therefore, I didn't comb my hair.

Which law is being demonstrated?

If my team wins the game, then they will be the champions.

My team is the champion.

Therefore, my team won the game.

Which law is being demonstrated?

If you go to the mall, then you will spend money.

You didn't spend any money today.

What is the logical conclusion?

If you don't feel well, then you stay home.

You feel well.

What is the logical conclusion?

How do you feel about the Laws of Logic now?

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

Statement:

Some ketchup is kissan.

Some ketchup is tops.

No jam is ketchup.

Conclusion

I. Some kissans are tops.

ll. Some tops are ketchup.

lIl. Some jams are kissan.

Statement:

Only a few Noise are Train

All Train are Eye

Only a few Eye are Music

Conclusion:

I:All Music can be Train

ll: No Noise is music

Statement:

Some studio are hall

All hall are room

Only room is bag

Conclusion:

I. Some bag are hall

ll. Some studio are room

Ill. All Studio can be hall

Statement:

Some squares are circles.

No circle is a triangle.

No line is a square

Conclusion

I. No triangle is a square.

ll. No line is a circle.

Statement:

All Petrol is Diesel

No Diesel is CNG

No CNG is LPG

Conclusion

I: All LPG can be Petrol

ll: Some Diesel are not LPG

Statement:

All songs are poems.

All poems are rhymes.

No rhyme is paragraph.

Conclusion:

I. All rhymes are poems.

ll. All Songs are rhymes.

Statement:

Some boys are Students

Some students are girls

No girl is a boy

Conclusion:

I. All boys being girls is a possibility

Il. All girls being boys is a possibility

Ill. Some boys are girls

.Statement:

Some A are B

Some B are D

Some Care A

Conclusion:

I. Some C are B

ll. Some D are not A

lll. No B is C

Statement:

Some stools are buns.

No bun is a globe.

All globes are hugs

Conclusion:

I. Some hugs are stools.

ll. Some globes are stools.

Ill. No hug is a stool.

Statement:

Some lakers are swans.

Some swans are wells.

Some wells are screens.

Conclusion:

I. Some screens are swans.

ll. Some wells are lakers.

Ill. Some screens are lakers

Statement:

All flaps are fingers.

All fingers are bails.

All bails are yens

Conclusion:

I. Some yens are fingers.

ll. Some bails are flaps.

Ill. Some yens are flaps

Statement:

All sinks are links.

All links are barns.

Some barns are oranges.

Conclusion:

I. Some oranges are links.

ll. Some barns are sinks.

Ill. Some oranges are sinks

Statement:

Only a few debits are credits.

A few credits are cash.

Conclusion:

I. Some cash are definitely not debits.

Il. All debits being cash is a possibility.

Ill. All debits being credits is a possibility.

Statement:

Only a few volumes are display.

Only a few screens are volumes

Conclusion:

I. Some screens are definitely not display.

ll. All display being screens is a possibility

Statement:

Only a few corners are nooks.

No nook is an edge.

No edge is a hole.

Conclusion:

I. All holes can never be corners.

Il. At least some nooks are holes.

Ill. Some edges can be corners.

If the sun is shining it is a beautiful day. If it is a beautiful day then we will go go hiking.

If you go to the swimming pool, then you will enjoy yourself. If you enjoy yourself, you will want to return.

Which law of logic is this?

If I clean the bathroom, then I don't have to do the dishes.

I cleaned the bathroom.

Therefore, I don't have to do the dishes.

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Statement 1: If I study for one hour each day, then I will score well on the exam

Statement 2: I will study from 6pm to 7pm tonite.

Write the if-then statement that follows from the pair of true statements.If chris goes to the movies, then Todd will go to the movies. If Todd goes to the movies, then Sarah will go to the movies.