If A = B and B = C, does A = C ?

[Caydr]

Does the above kind of question, usually found on IQ tests, confuse you? It confused me too, at first, until I realized the answer.

The answer is, "Impossible to tell."

Why? I'll give you a few examples.

Monkies (A) are Primates (B). Primates (B) are Animals (C). Monkeys (A) are Animals (C). In this case, A does equal C.

However, this isn't always the case.

The Johnsons (A) are a nuclear family. That means, their family consists of a husband, a wife, and 2.5 children. Anyhow, the Johnsons (A) are a Nuclear Family (B). Nuclear Families (B) are Common (C). However, the Johnsons (A) are not Common (C), because there's only one Johnson family. In this case, A does NOT equal C.

Another example:

Chris Rock (A) claims to be a comedian. Comedians (B) are Funny (C). However, Chris Rock (A) is not Funny (C).

[Min3mat]

monkeys ARE animals
claiming to be a comedian is different from being a comedian
the type of family 'the johnsons' is common though which is explicitely implied by the question
however i understand ur point. it holds for a few examples IRL but in maths A really does equal C (otherwise how the hell would partial fractions work! :))

[raikitsune]

as a question. the answer is yes. if you start putting theoretical examples to it many of the answers are no.

[maverick256]

well, depends how you define the relation =. If = is the common mathematical use of =, namely, the identity relation, then it is true. But there are plenty of relations out there that does not satisfy the transitive property (if a relates to b, and b relates to c, then a relates to c).

[Caydr]

Well, uh... really I just wanted to make fun of Chris Rock.

[maverick256]

I'm sorry, it's late at night here, so I'm really not thinking properly. Who's Chris Rock? (I'm culturally, er.... uninformed.....)

[SwiftSpear]

If all comedians are funny and Chris Rock is a comedian then chris rock is funny. You are misusing the = sign by defining it with a linguistic definition. "are" and "equals" are not the same. Nuclear familes cannot = common, the might "be" common and they "are common" but common is a trait of the nuclear family object, not an object that you can compare them against.

[Min3mat]

a triple line equals sign means 'identically equal to' the standard double line simply means 'equal to'

[maverick256]

Yeah, that's true. Shouldn't have called = the identity relation...

[SinbadEV]

as far as math goes(not trig, not topography, not geometry even)... if a=b and b=c then 0=b-a and 0=b-c therefore b-a=b-c therefore a=c... in formal logic... aka talking/arguing... IF a=b AND b=c THEN a doesn't neccessarily equal c... like you say, because a=b is true and b=c is true doesn't mean a=c is true... like you say... joe is ugly, ugly is an ajective but joe is not an adjective... a=b b=c a!=c...