Identify the Assumption (Conditional Logic) Flashcards
IDENTIFY THE ASSUMPTION:
Premise: X —> S
Conclusion: S
Premise: X —> S
Assumption: X
Conclusion: S
This argument is missing the trigger for the conditional: X. If we know that X is true, then that triggers the premise and allows us to conclude that S is true.
IDENTIFY THE ASSUMPTION:
Premise: H —> J
Conclusion: /H
Premise: H —> J
Assumption: /J
Conclusion: /H
This argument is missing the information that would trigger the contrapositive of the premise. Here, if we know that J is NOT true, then that would trigger the contrapositive of the premise, which allows us to conclude that H is NOT true.
IDENTIFY THE ASSUMPTION:
Premise: T —> /R
Conclusion: L —> /R
Assumption: L —> T
Premise: T —> /R
Conclusion: L —> /R
This new concept in the conclusion is L. We’re trying to conclude that L is sufficient for NOT R, so we want to know that L is sufficient to lead to T, which in turn leads to NOT R.
IDENTIFY THE ASSUMPTION:
Premise: E —> Z
Conclusion: E —> Q
Premise: E —> Z
Assumption: Z —> Q
Conclusion: E —>Q
The new concept in the conclusion is Q, and we’re trying to prove that E leads to Q. Since we already know that E leads to Z, we just need to show that Z leads to Q. That will allow us to conclude that E leads to Q.
IDENTIFY THE ASSUMPTION:
Premise: Y —> /B
Premise: R —> Q
Conclusion: R —> /Y
Premise: Y —> /B
Premise: R —> Q
Assumption: Q —> B
Conclusion: R —> /Y
We’re trying to conclude that R leads to NOT Y. One premise tells us that R leads to Q. So we want to get from Q to NOT Y. How can we do that? Well, the contrapositive of the first premise is B leads to NOT Y. So we want to connect Q to B. That would allow us to get from R to Q, which connects to B, which in turn leads to NOT Y.
IDENTIFY THE ASSUMPTION:
Premise: M —> Z
Premise: G
Conclusion: Z
Premise: M —> Z
Premise G
Assumption: G —> M
Conclusion: Z
We are trying to conclude that Z is true, and we have a premise that says M leads to Z. So that means we want to trigger that conditional; we want to know that M is true. The other premise is G. Since we want to know that M is true, we can add the assumption G leads to M. Since G is true, that means M is true, which, based on the first premise, means that Z is true.
IDENTIFY THE ASSUMPTION:
Premise: W
Conclusion: Y
Premise: W
Assumption: W —> Y
Conclusion: Y
We want to bridge the gap between the premise, W, and the conclusion, Y. So we want to know that W leads to Y.
IDENTIFY THE ASSUMPTION:
Premise: /Y —> /G
Premise: G
Conclusion: M
Premise: /Y —>/G
Premise: G
Assumption: Y —> M
Conclusion: M
The premises tell us that Y is true (because G is true, which triggers the contrapositive of the first premise). Given that we know Y is true, if we want to prove the conclusion that M is true, we want to know that Y leads to M. That would allow us to get from G, to Y (through the contrapositive of the first premise), to M (through the assumption).
IDENTIFY THE ASSUMPTION:
Premise: Y or F
Premise: F —> Z
Conclusion: C —> Z
Assumption: C —> /Y
Premise: Y or F
Premise: F —> Z
Conclusion: C —> Z
We want to prove that C leads to Z. Based on the second premise, we know that F leads to Z. So that means we want C to lead to F. But how do we get to F? Well, based on the first premise, if Y is NOT true, then that means F will be true, since we have to have at least one of Y or F. So if we can get C to lead to NOT Y, that will lead to F, which leads to Z.
IDENTIFY THE ASSUMPTION:
Premise: A -some- F
Conclusion: A -some- N
Premise: A -some-F
Assumption: F —> N
Conclusion: A -some- N
We want to prove that some A are N. Based on the premise, we already know that some A are F. So how do make those As into Ns? By adding that all F are N. If we add F —> N, then the As that are F also have to be Ns.
IDENTIFY THE ASSUMPTION:
Premise: R —> W
Conclusion: D —> /R
Premise: R —>W
Assumption: D —> /W
Conclusion: D —> /R
We want to prove that D leads to NOT R. We already know from the contrapositive of the premise that NOT W leads to NOT R. So we want D to lead to NOT W. If we add that assumption, then D gets to NOT W, which gets to NOT R.
