Binary Operation E-Book

 

Published by- Google

Binary Operation E-Book

A SMALL EXAMPLE FOR ALL THE STUDENTS

Question 1: Show that division is not a binary operation in N nor subtraction in N.

Answer : Let a, b ∈ N

Case 1: Binary operation * = division(÷)

–: N × N→N given by (a, b) → (a/b) ∉ N (as 5/3 ∉ N)

Case 2: Binary operation * = Subtraction(−)

–: N × N→N given by (a, b)→ a − b ∉ N (as 3 − 2 = 1 ∈ N but 2−3 = −1 ∉ N).

Question 2: Are all binary operations closed?

Answer: Many sets that you might be familiar to are closed under certain binary operators, whereas many are not. Thus, the set of odd integers remains closed under multiplication. For instance, the set of odd integers is not closed under addition, as the sum of two odd numbers is not always odd, actually, it is never odd.

Question 3: Is square root a binary operation?

Answer: A non-binary operation refers to a mathematical process which only requires one number to achieve something. Addition, subtraction, multiplication, and division are examples of binary operations. Similarly, examples of non-binary operations consist of square roots, factorials, as well as absolute values.

Question 4: What is the identity element in a binary operation?

Answer: An identity element or neutral element in binary operation refers to a special kind of element of a set with regards to a binary operation on that set, that leaves an element of the set unaffected when combined with it. We use this concept in algebraic structures like groups and rings.

Question 5: What is the binary overflow?

Answer: Overflow takes place when the magnitude of a number surpasses the range permitted by the size of the bit field. The sum of two identically-signed numbers may very well surpass the range of the bit field of those two numbers, and thus overflow may be a possibility in this case.

Read this PDF so you get much more about Binary Operation rules.