Daniel Mansfield

Intorduces students to the definition of a function $f:A\mapsto B$ as a subset of the Cartesian product $A\times B$.

Slightly harder introductory exercises about the power set.

Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.

Formative assessment to introduce the concepts of modular arithmetic.

Introductory exercises about set theory designed to prepare students for their first lectures on the subject.

Intorduction to proof and existence statements.

This question summarizes the definitions of surjective and injective, and applies them to prove the existance of an inverse.

A graphical introduction to the concept of even functions a symmery

A graphical introduction to the concept of even functions a symmery

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A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

Version I. Graph is quadratic

Version II. Graph is horizontal

Version III. Graph is cubic

Version IV. Graph is sinusoidal

Create a truth table for a logical expression of the form $((a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d))\operatorname{op4}e $ where each of $a, \;b,\;c,\;d,\;e$ can be one the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3},\;\operatorname{op4}$ one of $\lor,\;\land,\;\to$.

For example: $((q \lor \neg p) \to (p \land \neg q)) \lor \neg q$

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

Example of a universal statement over the integers and its negation

An introduction to terminology about the surjective property of a function.

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