Lesson Five: Logical Reasoning and Logic Games Flashcards
–LOGICAL REASONING–
Assumption
The unstated premise that, if stated, would make the argument true.
Assumption questions always refer to ______________ ____________, not ____________ ______________. Explain the difference between the two.
Necessary Assumptions; Sufficient Assumptions
Sufficient Assumptions are the unstated premises for Justify the Conclusion questions. Sufficient assumptions are assumptions that are sufficient to prove the conclusion logically follows (100%). For sufficient assumptions (in Justify the Conclusion questions) you will often see indicators like if, when, whenever, any, all, every, people who, in order to.
Necessary Assumptions are just the baseline, required assumptions that support the conclusion. (With necessary assumptions you’ll likely see indicators such as then, only if, must, required to, unless, until, except, without)
Think of an assumption as something that the ____________ and ___________ rest upon (TALKING ABOUT NECESSARY ASSUMPTIONS HERE); it is a __________ answer in a sense–something the author believed when forming the argument (just didn’t expressly state it).
If there’s a statement in the answer choice that the author only thinks _________ be true, or if there’s a statement that the author isn’t _________ committed to, then it’s not the right answer.
The assumption, that is your answer choice, should not contain any ________________ information.
premises; conclusion; minimalist; COULD; fully; extraneous
To (CHOOSE AN ANSWER CHOICE THTAT WOULD) support an argument, you must identify the ______________ and evaluate the _____________ of the ______________.
conclusion; validity; conclusion
Remember, when we talk about assumption questions, we’re always referring to necessary assumptions. Describe the wording in the the following Assumption questions that indicate necessary assumptions.
“Which one of the following is an assumption on which the argument depends?”
“The conclusion in the passage relies on which one of the following assumptions?”
“The conclusion cited does not follow unless.”
depends; relies; unless
Remember, there are Justify the Conclusion questions that use the words ____________ and ______________, but you should know the difference between these questions stems, and the ones you’ll encounter in an ______________ question. The assumptions used to answer a Justify question are ________________ assumptions (oftentimes using indicators such as ___, ____________, ____________, _______, _______, ___________, ____________ _____, _____ ____________ ______).
“assume”; “assumption”; assumption; sufficient; if; when; whenever; any; all; every; people who, in order to
Two Types of Assumptions in the Assumption Model
Supporter Assumptions
Defender Assumptions
Supporter Assumptions
Link the ideas in the premises and conclusion; their job is to fill the gap between the premises and conclusion.
Defender Assumptions
Assumptions (answer choices) that defend the premises and conclusion. Answers that eliminate any ideas or assertions that weaken the argument.
The Assumption Negation Technique
Keep in Mind: You can only use this technique with assumption questions, and you can’t use it until you’ve separated your answer choices into contenders and losers.
Once you’ve separated your answers into contenders and losers, and you’re trying to decide between your answer choices, use the Assumption Negation Technique.
Remember, your answer choice is a necessary assumption; the required unstated premise that the author relies upon to connect the ideas from the premises and conclusion. It’s meant to support the argument. So whatever answer choice weakens the author’s argument would be wrong (but the opposite of weakening, is supporting which is RIGHT).
Take your contender answer choices, and logically negate them. Whichever answer attacks/weakens the author’s argument is the correct answer choice.
Whichever answer choice doesn’t attack the author’s argument is incorect.
–LOGIC GAMES–
Grouping Games
Evaluates what variables in a game can and cannot be grouped together.
In Grouping Games, we do NOT focus on _______________, like you would in a ___________ game. Here we just assess what variables can be ____________ in the same group.
ordering; linear; placed
Example Problem: “A four-person research group is selected from 7 candidates - H, J, K, L, M, O, R. The group is selected according to the following restrictions:
- If J is selected, then R is selected.
- If R is selected, then H is not selected.
Diagram the rules for this game.
J → R
R → ̶H̶
Unified Grouping Theory
Grouping games can be broken down into three basic parts.
1. Defined
2. Undefined
3. Partially Defined
- Defined Grouping
Gives the exact number of variables to be selected for a grouping game.
Defined Grouping Games can be further broken down into Balanced, Unbalanced, Overloaded, Underfunded Games.
Ex. There are 5 students, each of which are candidates for a 3-person group project.
- Undefined Grouping
Does not give the exact number of variables to be selected for a grouping game.
OR
There are multiple possibilities of how many the variables can be selected.
Ex. A committee is being formed from 10 possible candidates.
- Partially Defined Grouping
Maximum and minimum number of variables to be selected for a group is given, and the exact number of variables for the group is NOT given.
Ex. There are at least five people who must be a part of the committee.
Diagramming Grouping Games:
Diagramming works the same for grouping games as it does linear games; they can use the same rules. Diagramming obviously, is done using sequence, conditional, and block rules.
Ex.
1st “If J is selected, then R is selected.”
2nd “If R is selected, then H is not selected.”
Diagram these grouping game rules, and the inference it forms.
J→R
R→ ̶H̶
J→R→ ̶H̶
Inference: J→ ̶H̶
Diagramming w/ the Double Not Arrow:
Ex.
1st “If J is selected, then R is selected.”
2nd “If R is selected, then H is not selected.”
Diagram these grouping game rules, and the inference it forms.
J → R
R → ̶H̶
Take the contrapositive of the 2nd rule: H → ̶R̶
The 2nd rule and it’s contrapositive necessarily mean if you have R, then you can’t have H, AND if you have H, then you can’t have R. So use the Double Not Arrows to represent this biconditional relationship.
R ←|→ H
J → R ←|→ H
J is always selected w/ R, but R is never selected with H. This allows you to infer…
J←|→ H
Linear vs. Grouping Symbolization:
When diagramming rules, linear games represent the adjacency of variables, whereas grouping games represent the association of variables.
Linear vs. Grouping Symbolization Example:
“H and J cannot be selected together.”
Give the Linear Game diagramming
Give the Grouping Game diagramming
Linear Game:
┍━─┓
┃ ̶H̶J̶ ┃
┗━─┛
Grouping Game:
H←|→ J
Hurdle the Uncertainty
Hurdle the Uncertainty is a technique for placing other variables that were selected for a game in the table, when you don’t know where to place other variables.
Ex. 1
Three Variables –A, B, and C– are available to fill two spaces.
Rule: A and B cannot be selected together.
Give the rules to the game, describe how to hurdle the uncertainty, and solve the game.
Defined, Overloaded Game.
You have two available spots: ___ ___
According to the rule:
A → ̶B̶
B → ̶A̶
So… A ←|→ B
So we know A and B can’t be selected to be in the same group, but two spots need to be filled.
So create a dual option between A and B to fill one slot (because only one of them can be the group), and, because all of this is the case, fill the other slot with C.
A͟/͟B͟ C͟
Ex. 2
Four Variables –A, B, C, D– are available to fill three spaces.
Rules: A, B, C cannot be selected together.
Give the rules to the game, describe how to hurdle the uncertainty, and solve the game.
Defined, Overloaded Game.
You have three available spots: ___ ___ ___
According to the rule, the exact combination of 3 of the 4 variables, A, B, and C, cannot be in the same.
So, to hurdle the uncertainty (given that we have variables that cannot be selected to be in the same group), we know only two of these variables can go in two of the available spots, but we don’t know which ones, so create a dual option across two of the slots for A, B, and C. And in the remaining third slot, D will be placed.
(A,B,C) D
___ ___ ___
Ex. 3
Five variables – A, B, C, D, E–are divided into two groups, a group of three and group of two.
Rules:
A and B cannot be in the same group.
C and D must be in the same group.
Give the rules to the game, describe how to hurdle the uncertainty, and solve the game.
Defined, Balanced Game.
You have five available spots, three available in one group, two available in another.
___
___ ___
___ ___
(3) (2)
Rules:
A ←|→ B
C ←→ D
From the rules we can gather that A and B Cannot be in the same group, but we don’t know where A or B go in exactly either the 3-group or 2-group. So to hurdle the uncertainty, we’ll use dual options A/B and B/A to be placed in a slot for each group. Of course, in the 3-group this only leaves to slots, and we know C and D are inseparable, so C and D will go in the three group, leaving E to be placed in the 2-group.
D
C E
A/B B/A
Ex. 4
Five variables –A, B, C, D, E– are available to fill three spaces.
Rules:
A and B cannot be selected together.
C and D cannot be selected together.
Give the rules to the game, describe how to hurdle the uncertainty, and solve the game.
Defined, Overloaded Game.
___ ___ ___
Rules:
A ←|→ B
C ←→ D
Hurdle the Uncertainty: you know A and B can’t be in the same group, place an A/B dual option in one of the slots.
You know C and D can’t be in the same group, place a C/D dual option in one of the slots.
This leaves E to be in the remaining 3rd slot.
A/B C/D E
____ _____ _____
