SOLUTION: Four men, Mr. Baker, Mr. Carpenter, Mr. Draper, and Mr. Smith, live in Logictown. One is a baker, one a carpenter, one a draper, and one a smith, but none follows the vocation corr

Question 1042040: Four men, Mr. Baker, Mr. Carpenter, Mr. Draper, and Mr. Smith, live in Logictown. One is a baker, one a carpenter, one a draper, and one a smith, but none follows the vocation corresponding to his name. A logician tries to find out who is who and obtains the following partially correct information:
Mr. Baker is the smith.
Mr. Carpenter is the baker.
Mr. Draper is not the smith.
Mr. Smith is not the draper.
If it is known that three of the four statements are false, who is the carpenter? (Hint:consider the four possible sets of truth values given for the statements in the table below)
I was given the following table:
Statement|I II III IV
1 |T F F F
2 |F T F F
3 |F F T F
4 |F F F T

If you could please explain everything it will be great because I am really lost
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I'm going to use the convention that upper case refers to a name and lower case refers to an occupation and the symbol <> means 'not equal'.

The four statements are then:

B = s
C = b
D <> s
S <> d

Let us assume that the first statement is true, so the other three are false.
Given that the four True statements are:

B = s
C <> b
D = s
S = d

But if C <> b, and because C = c is not allowed by the problem statement, C = d or C = s.  Either one of these statements contradicts D = s or S = d.  Therefore the assumption that B = s is false.

Next, let us assume that the second statement is true, and the other three are false.

The four true statements are then:

B <> s
C = b
D = s
S = d

Since B <> s, it must be true that B = c or B = d, hence Baker is the carpenter because B = d contradicts S = d.

Next, let us assume that the third statement is true, leading to:

B <> s
C <> b
D <> s
S = d

B <> s means B = c or B = d.  C <> b means C = s or C = d.  And D <> s means D = b or D = c.  B must equal c because B = d contradicts S = d.  Then D = b and C = s.  Again, Baker is the carpenter.

Lastly, let us assume that the fourth statement is true, leading to:

B <> s
C <> b
D = s
S <> d

Since D = s and C must then be d or s, C = d.  S <> d means S = b or S = c and B <> s means B = c or B = d, so S = b and B = c.  Again, Baker is the carpenter.

We don't know which of statements 2, 3, or 4 is true, but we do know for certain that Baker is the carpenter.

John

My calculator said it, I believe it, that settles it

RELATED QUESTIONS
Baker and co- Who is Who and Who lives Where? Messrs Carpenter, Baker and Mason live in... (answered by josgarithmetic,math_tutor2020)

solve. Round to the nearest tenth of necessary Mr. Endicott, Mr. Bookout, and Mr.... (answered by Theo)

Mr. Russo takes three minutes less than Mr. Lloyd to pack a case when each works alone.... (answered by ankor@dixie-net.com)

mr. (answered by richwmiller)

mr baker has 15 giants in his clan 8 are blue 7 pink. mr baker will randomly pick three... (answered by advanced_Learner)

Mr. Smith purchased $125.00 worth of spices and herbs. Because this was such a large... (answered by stanbon)

Mr. Smith has three times as many girls as boys in his class. Ms. Perry has twice as many (answered by Theo)

Mr. Smith is appointed as the principal of a school. In order to keep the building safe,... (answered by MathLover1)

Mr. Housenecht can do a piece of work in two and a half days and Mr. Warwick in three and (answered by TimothyLamb)