Math Midterm Review Notes

Vocabulary flashcards covering deductive vs. inductive reasoning, set theory operations and notation, sequence patterns, and logic statements.

Deductive Reasoning

Reasoning where a specific conclusion must follow from general information; if the first statements are true, the information guarantees that the conclusion has to be true.

Inductive Reasoning

Reasoning that uses specific examples or patterns to arrive at a likely conclusion or generalization, where the information does not guarantee the conclusion.

General Principle

A broad rule or statement that you start with and treat as true.

General Conclusion

A rule or generalization that you arrive at through reasoning.

Complement of a Set ($X'$)

The set containing everything in the universal set ($U$) that is NOT in the specified set ($X$).

Set Difference ($X' - Y$)

An operation where you take everything in the first set ($X'$) and remove anything that is also found in the second set ($Y$).

Cartesian Product ($A \times B$)

An operation where every element of set $A$ is paired with every element of set $B$.

Method of Successive Differences

A technique used to find patterns and determine the next number in a sequence by analyzing the differences between consecutive terms.

Opposite Pairs (Cube Folding)

Pairs of faces on an unfolded box that can never touch each other when the box is folded.

Listing Method

A method of specifying a set by writing out all of its individual elements within set braces.

Set-Builder Notation

A notation that describes a set by using a variable (such as $x$) followed by a rule or condition specifying the properties its elements must satisfy.

Element ($\in$)

An individual number or item inside of a set.

Subset ($\subseteq$)

A set relation indicating that one set is contained inside another set.

Proper Subset ($\subset$)

A relation where the first set is contained in the second set and the two sets are not identical (the first set is not equal to the second).

Intersection ($\cap$)

The set operation representing what two or more sets have in common (the overlapping elements).

Union ($\cup$)

The set operation that combines everything from the given sets without duplicates (representing 'OR').

Statement

A sentence that can be determined to be either TRUE or FALSE (opinions cannot be statements).

Negation

The opposite of a statement, which changes its truth value from true to false or vice versa.