Introduction to Logic solution – Analyzing Arguments

1 EXAMPLE 1
2 EXAMPLE 2
3 EXAMPLE 3
4 EXAMPLE 4
5 EXAMPLE 5
6 EXAMPLE 6
7 EXAMPLE 7
8 EXAMPLE 8
9 EXAMPLE 9
10 EXAMPLE 10
11 Related Posts

EXAMPLE 1

1) If second native is politician

2nd	politician
1st	politician
3rd	non-politician

two politicians

2) If second native is non-politician

2nd	non-politician
1st	non-politician
3rd	politician

one politician

EXAMPLE 2

1) second – red, third – red

First must have told what hat he wore – white

2) second – white, third – red

First could not tell.

Second must have told what hat he wore – white. Because first could not tell and third was red.

3) second – red, third – white

Second could not tell. Because second’s hat might have been white.

Third could tell what hat he wore. Because third’s hat must not have been red.

4) second – white, third – white

Second could not tell. Because second’s hat might have been red.

Third could tell what hat he wore. Because third’s hat must not have been red.

EXAMPLE 3

a. Mr. Robinson lives in Detroit.

f. The passenger living in Chicago has the same name as the brakeman.

	brakeman	fireman	engineer
Jones
Robinson	X
Smith

d. Smith once beat the fireman at billiards.

	brakeman	fireman	engineer
Jones
Robinson	X
Smith		X

b. The brakeman lives halfway between Detroit and Chicago.

c. Mr. Jones earns exactly $40,000 a year.

e. The brakeman’s next-door neighbor, one of the three passengers mentioned, earns exactly three times as much as the brakeman.

f. The passenger living in Chicago has the same name as the brakeman.

	brakeman	fireman	engineer
Jones	O	X	X
Robinson	X
Smith	X	X

brakeman, Mr. Smith = between Detroit and Chicago

Mr. Jones = Chicago

brakeman = Jones

	brakeman	fireman	engineer
Jones	O	X	X
Robinson	X	O	X
Smith	X	X	O

The engineer’s name is Smith

EXAMPLE 4

4. The employees of a small loan company are Mr. Black, Mr. White, Mrs. Coffee, Miss Ambrose, Mr. Kelly, and Miss Earnshaw. The positions they occupy are manager, assistant manager, cashier, stenographer, teller, and clerk, though not necessarily in that order. The assistant manager is the manager’s grandson, the cashier is the stenographer’s son-in-law, Mr. Black is a bachelor, Mr. White is twenty-two years old, Miss Ambrose is the teller’s stepsister, and Mr. Kelly is the manager’s neighbor.

Mr. Kelly is the manager’s neighbor.

	manager	assistant manager	cashier	stenographer	teller	clerk
Mr. Black
Mr. White
Mrs. Coffee
Miss Ambrose
Mr. Kelly	X
Miss Earnshaw

Miss Ambrose is the teller’s stepsister.

	manager	assistant manager	cashier	stenographer	teller	clerk
Mr. Black
Mr. White
Mrs. Coffee
Miss Ambrose					X
Mr. Kelly	X
Miss Earnshaw

The assistant manager is the manager’s grandson. (The assistant is not woman and the manager is not miss)

	manager	assistant manager	cashier	stenographer	teller	clerk
Mr. Black
Mr. White
Mrs. Coffee		X
Miss Ambrose	X	X			X
Mr. Kelly	X
Miss Earnshaw	X	X

The cashier is the stenographer’s son-in-law. (Cashier is not woman and stenographer is not miss)

	manager	assistant manager	cashier	stenographer	teller	clerk
Mr. Black
Mr. White
Mrs. Coffee		X	X
Miss Ambrose	X	X	X	X	X
Mr. Kelly	X
Miss Earnshaw	X	X	X	X

Mr. Black is a bachelor. (not cashier, stenographer, and manager)

The assistant manager is the manager’s grandson. (Mr. Black is not The assistant manager)

	manager	assistant manager	cashier	stenographer	teller	clerk
Mr. Black	X	X		X		X
Mr. White
Mrs. Coffee		X	X
Miss Ambrose	X	X	X	X	X
Mr. Kelly	X
Miss Earnshaw	X	X	X	X

Mr. White is twenty-two years old. (not stenographer and manager)

	manager	assistant manager	cashier	stenographer	teller	clerk
Mr. Black	X	X		X		X
Mr. White	X			X
Mrs. Coffee		X	X
Miss Ambrose	X	X	X	X	X
Mr. Kelly	X
Miss Earnshaw	X	X	X	X

Mrs. Coffee is the manager.

	manager	assistant manager	cashier	stenographer	teller	clerk
Mr. Black	X	X		X		X
Mr. White	X			X
Mrs. Coffee	O	X	X	X	X	X
Miss Ambrose	X	X	X	X	X
Mr. Kelly	X
Miss Earnshaw	X	X	X	X

Mr. Kelly is the stenographer.

Miss Ambrose is the clerk.

	manager	assistant manager	cashier	stenographer	teller	clerk
Mr. Black	X	X		X		X
Mr. White	X			X		X
Mrs. Coffee	O	X	X	X	X	X
Miss Ambrose	X	X	X	X	X	O
Mr. Kelly	X	X	X	O	X	X
Miss Earnshaw	X	X	X	X		X

Miss Earnshaw is the teller.

	manager	assistant manager	cashier	stenographer	teller	clerk
Mr. Black	X	X		X	X	X
Mr. White	X			X	X	X
Mrs. Coffee	O	X	X	X	X	X
Miss Ambrose	X	X	X	X	X	O
Mr. Kelly	X	X	X	O	X	X
Miss Earnshaw	X	X	X	X	O	X

Mr. Black is the cashier

	manager	assistant manager	cashier	stenographer	teller	clerk
Mr. Black	X	X	O	X	X	X
Mr. White	X		X	X	X	X
Mrs. Coffee	O	X	X	X	X	X
Miss Ambrose	X	X	X	X	X	O
Mr. Kelly	X	X	X	O	X	X
Miss Earnshaw	X	X	X	X	O	X

Mr. Black is the assistant manager.

	manager	assistant manager	cashier	stenographer	teller	clerk
Mr. Black	X	O	X	X	X	X
Mr. White	X	X	O	X	X	X
Mrs. Coffee	O	X	X	X	X	X
Miss Ambrose	X	X	X	X	X	O
Mr. Kelly	X	X	X	O	X	X
Miss Earnshaw	X	X	X	X	O	X

EXAMPLE 5

If Lefty’s Each of statements is true, true, and false.

		TRUE	FALSE
Lefty	I did not kill Torelli.	O
	I never owned a revolver in all my life.	O
	Spike did it.		O
Red	I did not kill Torelli.
	I never owned a revolver.
	The others are all passing the buck.
Dopey	I am innocent.
	I never saw Butch before.
	Spike is guilty.
Spike	I am innocent.
	Butch is the guilty one.
	Lefty did not tell the truth when he said I did it.
Butch	I did not kill Torelli.
	Red is the guilty one.
	Dopey and I are old pals.

Spike is innocent.

		TRUE	FALSE
Lefty	I did not kill Torelli.	O
	I never owned a revolver in all my life.	O
	Spike did it.		O
Red	I did not kill Torelli.
	I never owned a revolver.
	The others are all passing the buck.
Dopey	I am innocent.	O
	I never saw Butch before.	O
	Spike is guilty.		O
Spike	I am innocent.	O
	Butch is the guilty one.		O
	Lefty did not tell the truth when he said I did it.	O
Butch	I did not kill Torelli.
	Red is the guilty one.
	Dopey and I are old pals.

Dopey and Butch are not old pals.

		TRUE	FALSE
Lefty	I did not kill Torelli.	O
	I never owned a revolver in all my life.	O
	Spike did it.		O
Red	I did not kill Torelli.
	I never owned a revolver.
	The others are all passing the buck.
Dopey	I am innocent.	O
	I never saw Butch before.	O
	Spike is guilty.		O
Spike	I am innocent.	O
	Butch is the guilty one.		O
	Lefty did not tell the truth when he said I did it.	O
Butch	I did not kill Torelli.	O
	Red is the guilty one.	O
	Dopey and I are old pals.		O

Red is the guilty one.

		TRUE	FALSE
Lefty	I did not kill Torelli.	O
	I never owned a revolver in all my life.	O
	Spike did it.		O
Red	I did not kill Torelli.		O
	I never owned a revolver.	O
	The others are all passing the buck.	O
Dopey	I am innocent.	O
	I never saw Butch before.	O
	Spike is guilty.		O
Spike	I am innocent.	O
	Butch is the guilty one.		O
	Lefty did not tell the truth when he said I did it.	O
Butch	I did not kill Torelli.	O
	Red is the guilty one.	O
	Dopey and I are old pals.		O

Red is the whodunnit.

EXAMPLE 6

6. Mr. Short, his sister, his son, and his daughter are fond of golf and often play together. The following statements are true of their foursome:
a. The best player’s twin and the worst player are of the opposite sex.
b. The best player and the worst player are the same age.

Which one of the foursome is the best player?

possible twin couple: (Mr. Short, his sister), (his son, his daughter)

possible same age: (Mr. Short, his sister), (his son, his daughter) or (his sister, his son, his daughter)

The best player: his daughter

The best player’s twin: his son

The worst player: his sister

EXAMPLE 7

		TRUE	FALSE
Otto	I was in Chicago when Kilraine was murdered.
	I never killed anyone.
	The Kid is the guilty one.	O
	Mickey and I are pals.
Curly	I did not kill Kilraine.
	I never owned a revolver in my life.
	The Kid knows me.
	I was in Detroit the night of March 17.
Slim	Curly lied when he said he never owned a revolver.
	The murder was committed on St. Patrick’s Day.
	Otto was in Chicago at this time.
	One of us is guilty.
Mickey	I did not kill Kilraine.
	The Kid has never been in Pontiac.
	I never saw Otto before.
	Curly was in Detroit with me on the night of March 17.
The Kid	I did not kill Kilraine.		O
	I have never been in Pontiac.
	I never saw Curly before.
	Otto erred when he said I am guilty.		O

If ‘The Kid is the guilty one.’ is true, ‘I did not kill Kilraine.’ and ‘Otto erred when he said I am guilty.’ are false. Impossible.

‘The Kid is the guilty one.’ is FALSE.

		TRUE	FALSE
Otto	I was in Chicago when Kilraine was murdered.	O
	I never killed anyone.	O
	The Kid is the guilty one.		O
	Mickey and I are pals.	O
Curly	I did not kill Kilraine.
	I never owned a revolver in my life.
	The Kid knows me.
	I was in Detroit the night of March 17.
Slim	Curly lied when he said he never owned a revolver.		O
	The murder was committed on St. Patrick’s Day.	O
	Otto was in Chicago at this time.	O
	One of us is guilty.	O
Mickey	I did not kill Kilraine.
	The Kid has never been in Pontiac.
	I never saw Otto before.
	Curly was in Detroit with me on the night of March 17.
The Kid	I did not kill Kilraine.	O
	I have never been in Pontiac.
	I never saw Curly before.
	Otto erred when he said I am guilty.	O

		TRUE	FALSE
Otto	I was in Chicago when Kilraine was murdered.	O
	I never killed anyone.	O
	The Kid is the guilty one.		O
	Mickey and I are pals.	O
Curly	I did not kill Kilraine.		O
	I never owned a revolver in my life.	O
	The Kid knows me.	O
	I was in Detroit the night of March 17.	O
Slim	Curly lied when he said he never owned a revolver.		O
	The murder was committed on St. Patrick’s Day.	O
	Otto was in Chicago at this time.	O
	One of us is guilty.	O
Mickey	I did not kill Kilraine.	O
	The Kid has never been in Pontiac.	O
	I never saw Otto before.		O
	Curly was in Detroit with me on the night of March 17.	O
The Kid	I did not kill Kilraine.	O
	I have never been in Pontiac.	O
	I never saw Curly before.		O
	Otto erred when he said I am guilty.	O

Curly killed Kilraine.

EXAMPLE 8

Balancing six balls

HR1(heavy), LR2(light), HG1(heavy), LG2(light), HB1(heavy), LB2(light)

Step 1. one ball of Reds with one ball of Greens vs. one ball of Blues with one ball of Greens

HR1(heavy), HG1(heavy)	LG2(light), HB1(heavy)
heavier
HR1(heavy), HG1(heavy)	LG2(light), LB2(light)
heavier
LR2(light), HG1(heavy)	LG2(light), LB2(light)
heavier

The heavier side must include ‘HG1(heavy)’

Step 2. two balls of Greens vs. the others

HG1(heavy), LG2(light)	HR1(heavy), HB1(heavy)
	heavier
HG1(heavy), LG2(light)	HR1(heavy), LB2(light)
equal
HG1(heavy), LG2(light)	LR2(light), LB2(light)
heavier

You can identify the heavier and the lighter balls in all three pairs.

Another.

Step 1. one ball of Reds with one ball of Greens vs. one ball of Blues with one ball of Greens

LR2(light), HG1(heavy)	LG2(light), HB1(heavy)
equal

Step 2. one ball of Greens vs. one ball of Greens

HG1(heavy)	LG2(light)
heavier

You can identify the heavier and the lighter balls in all three pairs.

EXAMPLE 9

The first native cannot be non-politician, because the politician never tell the truth. If they are all politicians, “We are all politicians.” is not the true. The first native is the politician.

The second native says, “No, just two of us are politicians.”

1) If the second native is the politician

first	the politician
second	the politician
third	the politician? the non-politician?

If the third native is the politician, the first told the truth. Impossible.

If the third native is not the politician, the second told the truth. Impossible.

2) If the second native is not the politician

first	the politician
second	the non-politician
third	the politician

If the third native is not the politician, the third is the politicion.

“That isn’t true either.” is not the true.

EXAMPLE 10

Yes.