Definitions

Question 1

Define a subset.

Answer 1

A is a subset of B if (for all x)(x in A implies x is in B)

Question 2

Define Universal Set

Answer 2

The set of all elements is a set or group under consideration.

Question 3

Index Set

Answer 3

A set whose members label members of another set.

Question 4

Cartesian Product

Answer 4

A x B = {(x,y)| x is in A, y is in B}

Question 5

Relation on A

Answer 5

A relation on A is a subset of A x A.

Question 6

Partial Order

Answer 6

A relation on S with properties of being reflexive, anti-symmetric and transitive.

Question 7

Function

Answer 7

A relation from A to B in which each member of A appears exactly once as a first component.

Question 8

Injective Function (one to one)

Answer 8

Let f: A -> B. Then f is injective if f(a) = f(b) thus implies a = b.

Question 9

Surjective Function (onto)

Answer 9

Let f: A -> B. Then f is surjective if the codomain and range of f are the same. That is B = {f(x)|x is in A}.

Question 10

Bijective Function

Answer 10

A function that is both injective and surjective.

Question 11

T/F. The composition of two bijective functions is bijective.

Answer 11

True.

Question 12

Bezouts Theorem.

Answer 12

Let a and b be nonzero integers and let d=gcd(a,b). Then there exists integers m and n such that ma + nb = d.

Question 13

Valid Argument

Answer 13

The conjunction of the first n statements is said to imply the final statement. Thus P1^P2^…Pn => Q.

Question 14

Variable

Answer 14

A symbol that stands for a member of a collection.

Question 15

Predicate

Answer 15

A statement that describes the property of a variable.

Question 16

Define IVT

Answer 16

Suppose f is a continuous function on [a,b], and let N be between f(a) and f(b), where f(a) != f(b). Then there exists c in (a,b) such that f(c)=N.