MAT 224 - Foundations of Higher Mathematics

MAT 224 - FOUNDATIONS OF HIGHER MATHEMATICS

FINAL EXAM STUDY GUIDE

Chapter 14

Be able to state the formal definitions of the following terms: function, one-to-one, range, and co-domain.
Be able to determine if something is a function (given as either a set of ordered pairs, an algebraic function, or a diagram) .
Be able to state the domain and range of a given function.
Be able to state the inverse of a given function and then determine if it is also a function.
Be able to determine if a given function is "from," one-to-one, and onto.
Be able to give examples of functions that have one property but not another (ex: onto but not one-to-one).
Be able to state the reasons in a proof involving functions.
Be able to explain what a one-to-one correspondence is.

Old Stuff

Be able to complete an abbreviated truth table.

Be able to state the reasons for a proof involving implications, conjunctions, negations, quantifiers, etc.

Be able to state DeMorgan's Laws.

Be able to negate statements.

Be able to give the reasons in a proof involving even/odd integers.

Be able to state the induction hypothesis and "must show" for a statement involving the natural numbers.

Be able to find unions, intersections, complements, etc. of given sets.

Be able to give the formal definitions of a relation and a Cartesian product.

Be able to determine if a given relation has the reflexive, symmetric, and transitive properties.

Be able to find the ordered pairs belonging to a described equivalence relation.

Be able to state the formal definition of a partition.

Be able to determine the partition induced by a given equivalence relation on a set.

Be able to determine the equivalence relation induced by a given partition of a set.




		MAT 224 - FOUNDATIONS OF HIGHER MATHEMATICS
	FINAL EXAM STUDY GUIDE Chapter 14 Be able to state the formal definitions of the following terms: function, one-to-one, range, and co-domain. Be able to determine if something is a function (given as either a set of ordered pairs, an algebraic function, or a diagram) . Be able to state the domain and range of a given function. Be able to state the inverse of a given function and then determine if it is also a function. Be able to determine if a given function is "from," one-to-one, and onto. Be able to give examples of functions that have one property but not another (ex: onto but not one-to-one). Be able to state the reasons in a proof involving functions. Be able to explain what a one-to-one correspondence is. Old Stuff Be able to complete an abbreviated truth table. Be able to state the reasons for a proof involving implications, conjunctions, negations, quantifiers, etc. Be able to state DeMorgan's Laws. Be able to negate statements. Be able to give the reasons in a proof involving even/odd integers. Be able to state the induction hypothesis and "must show" for a statement involving the natural numbers. Be able to find unions, intersections, complements, etc. of given sets. Be able to give the formal definitions of a relation and a Cartesian product. Be able to determine if a given relation has the reflexive, symmetric, and transitive properties. Be able to find the ordered pairs belonging to a described equivalence relation. Be able to state the formal definition of a partition. Be able to determine the partition induced by a given equivalence relation on a set. Be able to determine the equivalence relation induced by a given partition of a set.