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# Fundamentals

### Rules, Formulas, Indicators

Logical Reasoning problems are made up of three components: stimulus, question stem, and a set of five answer choices
Two types of Logical Stimuli appear on the test: Argument and Set of Facts
Argument Consists of a conclusion and a set of premises given in support of that conclusion.
Set of Facts Is a group of statements from which no conclusion is explicitly drawn.
Valid Conclusion/Valid Inference Is a statement that must be true according to the premises.
Invalid Conclusion Is a statement that is not necessarily true according to the premises.
Many arguments require assumptions or unstated premises
Structural Indicators Certain words and phrases that do not constitute part of the subject matter being discussed in a sentence; instead they function as structural indicators that create relationships between words and phrases.
Conclusions Are often introduced by words and phrases such as therefore, thus, hence, consequently, so, it follows, or it can be concluded that.
Premises Are often introduced by words and phrases such as because, since, or proven by the fact that.
Sufficient Condition What is enough to make something true.
Necessary Condition What is required to make something true.
Incorrect Negation of a conditional statement is formed by negating both terms in that statement. The incorrect negation of any statement is different in meaning from that statement.
Incorrect Reversal Conditional statement is formed by reversing bother terms in that statement. The incorrect reversal of any statement is different in meaning from that statement.
Contrapositive Conditional statement is formed by reversing and negativing both terms in the statement. The Contrapositive of any statement is identical in meaning to that statement.
And/Or Rule A compound principle is a conditional statement that includes either multiple sufficient conditions or multiple necessary conditions.
And/Or Rule Converting the positive form of a compound principle into it's contrapositive form requires changing every and to or and changing every or to and.
Positive and Contrapositive There are only two apply a general principle to a specific case: applying the positive form of the principle or applying the contrapositive form of the principle.
If Formula The part of the statement that is introduced by if constitutes the sufficient conditions. The other part of the statement constitutes the necessary condition.
If Formula When, Whenever, Where, Wherever
Only If Formula The part of the statement that is introduced by only if constitutes the necessary condition. The other part of the statement constitutes the sufficient condition.
Only If Formula Only when, Only where, *Only by itself does not always introduce a necessary condition.
All Formula The part of the statement that is introduced by all constitutes the sufficient condition. The other part of the statement constitutes the necessary condition. The All Formula applies only to statements that begin with all.
All Formula Each, Every, Any
No Formula The part of the statement that is introduced by no constitutes the sufficient condition. The negation of the other part of the statement constitutes the necessary condition.
No Formula None
Unless Formula The part of the statement that is introduced by unless constitutes the necessary condition. The negation of the other part of the statement constitutes the sufficient condition.
Not Both Formula One of the variables (it does not matter which one) constitutes the sufficient condition. The negation of the other variable constitutes the necessary condition.
Either Or Formula The negation of one of the variables (it does not matter which one) constitutes the sufficient condition other variable constitutes the necessary condition. The expression either...or implies that at least one of two given variables must be present.