Macm 101 - Study guides, Class notes & Summaries

SetUnordered collection of objects. (No rigorous definition exists because there is no more general concept than sets - 'naive set theory') Can be described by listing all elements or using set builder Axiomatic Set Theory*More formalized definition of sets Elements/MembersThe objects in a set a ∈ A - a is an element of A, a belongs to A a ∉ A - a is not an element of A, a does not belong to A Set BuilderNotation for sets {x | P(x)}, the set of all x such that P(x) {x | there is ...

Lecture 14: Relations The connection between things or people Cartesian Product The Cartesian product of sets A and B, denoted by A × B, is the set of all *ordered pairs* of elements from A and B A × B = { (a,b) | a ∈ A, b ∈ B } These are two dimensional Ordered pair The elements of the Cartesian product are ordered pairs. In particular, (a,b) = (c,d) if and only if a = c and b = d Its a pair of numbers that can be used to locate a point on a coordinate plane K-tuples An ordered ...

Use of Logic (Mathematics & Rhetoric): 1) Give _________meaning to statements 2) Distinguish between ________ and ________ arguments 3) Provide ________ of "correct" reasoning specific, valid, invalid, rules (Lec. 2) Use of Logic (Computing): 1) Derive new____/knowledge from existing facts 2) Design of _______ _________ 3) Construction of ________ __________ 4) Verification of ________ of programs and circuit design 5) ____________ data, computer circuits, computer programs, correctn...

MACM 101 Midterm 2 Questions with 100% Correct Answers Lecture 14: Relations - The connection between things or people Cartesian Product - The Cartesian product of sets A and B, denoted by A × B, is the set of all *ordered pairs* of elements from A and B A × B = { (a,b) | a ∈ A, b ∈ B } These are two dimensional Ordered pair - The elements of the Cartesian product are ordered pairs. In particular, (a,b) = (c,d) if and only if a = c and b = d Its a pair of numbers that can be used ...

MACM 101 Set Theory Questions with 100% Correct Answers Set - Unordered collection of objects. (No rigorous definition exists because there is no more general concept than sets - 'naive set theory') Can be described by listing all elements or using set builder Axiomatic Set Theory* - More formalized definition of sets Elements/Members - The objects in a set a ∈ A - a is an element of A, a belongs to A a ∉ A - a is not an element of A, a does not belong to A Set Builder - Notation ...

MACM 101 Midterm 1 Questions with 100% Correct Answers (Lec. 2) Use of Logic (Mathematics & Rhetoric): 1) Give _________meaning to statements 2) Distinguish between ________ and ________ arguments 3) Provide ________ of "correct" reasoning - specific, valid, invalid, rules (Lec. 2) Use of Logic (Computing): 1) Derive new____/knowledge from existing facts 2) Design of _______ _________ 3) Construction of ________ __________ 4) Verification of ________ of programs and circuit design...

Lecture 14: Relations The connection between things or people Cartesian Product The Cartesian product of sets A and B, denoted by A × B, is the set of all *ordered pairs* of elements from A and B A × B = { (a,b) | a ∈ A, b ∈ B } These are two dimensional Ordered pair The elements of the Cartesian product are ordered pairs. In particular, (a,b) = (c,d) if and only if a = c and b = d Its a pair of numbers that can be used to locate a point on a coordinate plane K-tuples An ordered ...

SetUnordered collection of objects. (No rigorous definition exists because there is no more general concept than sets - 'naive set theory') Can be described by listing all elements or using set builder Axiomatic Set Theory*More formalized definition of sets Elements/MembersThe objects in a set a ∈ A - a is an element of A, a belongs to A a ∉ A - a is not an element of A, a does not belong to A Set BuilderNotation for sets {x | P(x)}, the set of all x such that P(x) {x | there is ...

(Lec. 2) Use of Logic (Mathematics & Rhetoric): 1) Give _________meaning to statements 2) Distinguish between ________ and ________ arguments 3) Provide ________ of "correct" reasoning specific, valid, invalid, rules (Lec. 2) Use of Logic (Computing): 1) Derive new____/knowledge from existing facts 2) Design of _______ _________ 3) Construction of ________ __________ 4) Verification of ________ of programs and circuit design 5) ____________ data, computer circuits, computer programs...