Hexadecimal to Octal to Binary Notation

Give a procedure for converting from the hexadecimal expansion of an integer to its octal expansion using binary notation as an intermediate step. keywords: notations

Ordered Pairs and Sets and Set Operations ( Complement, Union and Intersection )

1. a) Recall that ordered pairs must have the property that (x,y) = (u,v) if and only if x = u and y = v. Prove that {{x}, {x,y}} = {{u}, {u,v}} if and only if x = u and y = v. Therefore, although we know that (x,y) does not equal {x,y} , we can define the ordered pair (x,y) as the set {{x}, {x,y}}. b) Show by an example that we cannot define the ordered triple (x, y, z) as the set {{x}, {x,y}, {x,y,z}} 2. Which of the following are binary or unary operations on the given sets? For those that are not, where do they fail? a) x ◦ y = 1/x if x is positive S = set of all real numbers 1/(-x) if x is negative b) x ◦ y = xy (concatenation); S = set... click for more

Sets and Set Operations

4. Let A = {a, {a}, {{a}}} B = {ø, {a}, {a, {a}}} C = {a} Be subsets of S = {ø, a, {a}, {{a}}, {a, {a}}}. Find a) A C b) B C’ c) A B d) ø B e) (B C) A f) A’ B g) {ø} B 5. Let A = {x | x is the name of a former president of the US} B = {Adams, Hamilton, Jefferson, Grant} C = {x | x is the name of a state} Find: a) A B b) A C c) B C 6. Consider the following subsets of the set of all students: A = set of all computer science majors B = set of all physics majors C = set of all science majors D = set of all female students Using set operatio... click for more

Questions about ordered pairs, ordered triples, binary/unary operations, postfix notation

1. Recall that ordered pairs must have the property that (x,y) = (u,v) if and only if x = u and y = v. a) Prove that {{x}, {x,y}} = {{u}, {u,v}} if and only if x = u and y = v. Therefore, although we know that (x,y) does not equal {x,y} , we can define the ordered pair (x,y) as the set {{x}, {x,y}}. b) Show by an example that we cannot define the ordered triple (x, y, z) as the set {{x}, {x,y}, {x,y,z}} 2. Which of the following are binary or unary operations on the given sets? For those that are not, where do they fail? a) x ◦ y = 1/x if x is positive S = set of all real numbers 1/(-x) if x is negative b) x ◦ y = xy (concatenation); S = se o... click for more

Finding an Unknown Matrix Using an Inverse

Find a matrix A such that ┌ ┐ ┌ ┐ | 1 3 2 | | 7 1 3 | | 2 1 1 | A= | 1 0 3 | | 4 0 3 | | -1 -3 7 | └ ┘ └ ┘