An X can be a Y.
A Y can be a Z.
Therefore, an X can be a Z.
Are these valid?
All As are Bs. All Bs are Cs.
Some As are Bs. All Bs are Cs.
No As are Bs. All Bs are Cs.
Some As are not Bs. All Bs are Cs.
All As are Bs. Some Bs are not Cs.
All As are Bs Some As are Bs All Bs are Cs All Bs are Cs a = b = c a = b = c (b)= c (a) (b)= c (c) (c) Conclusion: All As are Cs Some As are Cs
No As are Bs Some As are not Bs All As are Bs All Bs are Cs All Bs are Cs Some Bs are not Cs a a a = b ----------- ----------- ------------ b = c (a) b = c (a) = b = c (c) (c) (b) = c a a (c) a (c) (b) ----------- ----------- ------------ b = c (a) b = c (a) = b c a = b c a (c) ----------- b = c Some Cs are not As No conclusion No conclusion
1. There is a king in the hand or there is an ace in the hand, or both.
2. There is a queen in the hand or there is an ace in the hand, or both.
Which is more likely to be in the hand, the king or the ace?
k | |
a | |
k | a |
There is a queen in the hand or there is an ace in the hand, or both.
q | |
a | |
q | a |
K |
L |
2 |
4 |
Rule to test:
If K, then 2.
Which cards must you turn over?
A1 | A2 | A3 |
B1 | B2 | B3 |
C1 | C2 | C3 |
Test: If A, then 2.
Which cards would you ask about to find out
whether this rules holds for all the cards?
(S is asked whether an A I and an A3 would be informative
in the unnegated multi-card task.)
S: No. Because... I was looking for A2 only.
E: But your goal is to find out ii the rule is true
or false. If there was A I or A3 in there, would that be
informative...?
S: No.
E: If the agent came back and said there was an A 1
and an A3 in the pouch, do you think that the rule would be true?
S: Yes.
E: You think it would?
S: Yes.
E: Even though there are As that don't have 2s on them.
S: Yes. Because.. the rule says if there is an A then there
is also a 2. It doesn't say there couldn't be an Al or an A3.
Theorem:
A cat has nine tails.
Proof:
No cat has eight tails.
A cat has one tail more than no cat.
Therefore, a cat has nine tails.