Discrete Mathematics - Binary Operations

Question 1

What is a Binary Operation

Answer 1

An operation that takes in 2 inputs from a set and returns an output from the same set.

Question 2

What does it mean for an operation to be closed

Answer 2

When the output is in the same set as the two inputs.

Question 3

What does it mean for an operation to be commutative

Answer 3

If a * b = b * a ; for all values a and b

Question 4

What does it mean for an operation to be associative

Answer 4

If (a * b) * c = a * (b * c); for all values a, b and c

Question 5

What is the identity element (e)

Answer 5

an element in a set that generates that when operated with outputs the non-identity input: e * a = a * e = a

Question 6

What is an inverse element

Answer 6

The element such that when applied to the original element outputs the identity element (e): a * a⁻¹ = a⁻¹ * a = i

Question 7

What is a self inverse

Answer 7

when a⁻¹ = a

Question 8

What are the 2 assumed commutativity, associatively laws

Answer 8

• Comutativity of addition and multiplication
• Associativity of matrix multiplication, addition and, multiplication

Question 9

How do you find the identity element in a cayley table

Answer 9

Look for the column that doesn’t change

Question 10

How do you find the inverses of the elemnts in a Cayley Table

Answer 10

Look along the row of the element, the inverse is the column heading that applied to the element give the identity element