Math 1103 Unit 1 Study Guide Review

Vocabulary and key concepts from the Math 1103 Unit 1 Study Guide, covering logic, set theory, probability, and counting principles.

Conditional statement

A logical statement represented symbolically as $p \rightarrow q$.

Converse

The logical variation of a conditional statement where the hypothesis and conclusion are swapped, represented as $q \rightarrow p$.

Inverse

The logical variation of a conditional statement where both the hypothesis and conclusion are negated, represented as $\sim p \rightarrow \sim q$.

Contrapositive

The logical variation of a conditional statement where the hypothesis and conclusion are both swapped and negated, represented as $\sim q \rightarrow \sim p$.

Logical Equivalence of $(A \cap B \cap C)^{'}$

According to the Venn diagram identity in the notes, the equivalent expression is $A' \cup B' \cup C'$.

Conditional identity

The logical property stating that $p \rightarrow q$ is equivalent to $\sim p \lor q$.

Zero Probability

The probability assigned to an impossible event, such as spinning a $14$ on a spinner numbered $1$ to $7$ ($P(s=14)=0$).

Probability of One

The probability assigned to a certain event, such as spinning a number less than or equal to $10$ on a spinner numbered $1$ to $10$ ($P(s \leq 10)=1$).

Set $A \cap B'$

The set containing elements that are located in $A$ but are not in $B$.

Set $B \cap A'$

The set containing elements that are located in $B$ but are not in $A$.

Compound logic statement: $(b \wedge x) \rightarrow a$

The symbolic form for the statement: 'If it is bedtime and we go to sleep, then the lights are off.'

Disjunction truth value

A logical 'or' statement ($\lor$) that is true if at least one component is true; for example, if $\sim a$ is True and $e$ is False, $\sim a \lor e$ is True.

Car configurations calculation

The method to find total combinations for $3$ independent binary features (sunroof, navigation, heated seats) calculated as $2^3 = 8$.