# Categorical logic: Some A are B. All B are C. Therefore, All A are C. [closed]

If Some tees are moos and all moos are yees are all tees yees? It is an IQ test question ... I said Yes but I am not 100% sure if I got it right.

• Some black things are cats. All cats meow. Therefore, all black things meow. Oct 12 '15 at 8:45
• Some A are B. All B are C. Therefore, Some A are C. Oct 12 '15 at 10:11
• Take the special case B = C. Your suggestion means this would also be true: Some A are B. All B are B. Therefore, all A are B. Oct 12 '15 at 22:30
• Thank you everyone for your help. I dod get mixed yes's and no's. Both make sense but I think the right answer is No. That all tees are not yees. : ) Oct 13 '15 at 3:40
• The important question is not "What's the right answer?" but "Where did you go wrong?". We can't answer this if we don't know your reasoning. What was your argument for "yes"? Oct 15 '15 at 6:11

Some animals are lions. All lions are yellow. Therefore, all animals are yellow.

No, this is wrong. We could get into the formal logic of it, and mathematical formulas that absolutely prove that this is wrong, but to be honest, this is too trivial for such a heavy handed approach.

In questions like this, the easiest is to give a counterexample.

Take A = N (i.e., the natural numbers: (0), 1, 2, 3, 4, ...)

Then, some As are multiples of 10.

All multiples of 10 are multiples of 2.

However, not all As are multiples of 2 (take e.g. 37).

• To be honest, in questions like these, it's easiest to give a real world example. Oct 12 '15 at 10:16
• @Davor you could make it real world by saying "1 cow", "2 cows", etc. if that helps you.
– user2953
Oct 12 '15 at 10:18

The answer is "No". You cannot exclude that some tees exist which are not moos; hence you cannot conclude that these tees are yees.

B and C have the property X in common, and are thus equal in terms of the property X. 'All B are C' can be thought of as 'B=C', which means that you have:

Some A are B. Therefore, All A are B.

As you can see it is a contradiction.

'Some' ≠ 'All'

If we replace A with 'candies in the bag' and B with 'Skittles [sour]', C with 'sour' we get:

Some candies in the bag are Skittles. All Skittles [sour] are sour. Therefore all candies in the bag are sour.

It might be true that all candies in the bag happened to be sour, but we cannot deduce that all candies in the bag are (in fact) sour.

You are given:

Some tees are moos

and

All moos are yees

Now, the second sentence is telling us that moos are also yees; that is if something is a moo, then it is also a yee. This means you can substitute moo by yee in the first sentence.

And when you do that, you get the following sentence:

Some tees are yees

So the answer is no, not all tees are yees - only some are!

• Now that makes a lot of sense : ) Oct 17 '15 at 20:28

Could go either way depending on set order, wording, or if any of the A,B,or C is an adjective, noun or verb. Ex. 1 "Some animals are cats, all cats are mortal," then true, "all animals are mortal." Assuming you believe all living things die. Ex.2 "Some animals are cats, all cats are mammals," then, " all animals are mammals," is a false statement.

BTW,in rebuttal to a previous post, not all lions are yellow, some are albinos. I'm not trying to be cute, just showing how important the wording is when it comes to the "if some As are Bs, all Bs are Cs, then all As are Cs" question.

• You're actually tricking yourself on this one. You're adding in extra premises that make the argument work rather than working with the premises that exist. The argument as worded (some A are B. All B are C. Therefore, All A are C) does not in a truth-preserving (valid) way yield the conclusion. You're revised version "Some A are B. All B are C. All A are C. Therefore Some A are C " is valid but trivial and meaningfully distinct from the OPs supplied argument. Jan 16 '16 at 4:44