# Ex 1.4 ,1

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 1.4 ,1 Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (i) On Z+, define * by a * b = a − b a * b = a − b. Here, a ∈ Z+ & b ∈ Z+ i.e. a & b are positive integers Let a = 2, b = 5 2 * 5 = 2 – 5 = –3 But –3 is not a positive integer i.e. –3 ∉ Z+ Hence, * is not a binary operation Ex 1.4, 1 Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (ii) On Z+, define * by a * b = ab a * b = a Here, a ∈ Z+ & b ∈ Z+ i.e. a & b are positive integers For every positive integer a & b, ab is also a positive integer. Hence, * is a binary operation on Z+. Ex 1.4, 1 Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (iii) On R, define * by a * b = ab2 a * b = ab2 For every real number a & b, ab2 is also a real number. Hence, * is a binary operation on R Ex1.4, 1 Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (iv) On Z+, define * by a * b = |a − b| a * b = |a − b|. Here, a ∈ Z+ & b ∈ Z+ i.e. a & b are positive integers For every a & b, |a − b| is also a positive integer. Hence, * is a binary operation on Z+. Ex 1.4, 1 Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (v) On Z+, define * by a * b = a a * b = a Here, a ∈ Z+ & b ∈ Z+ i.e. a & b are positive integers For every positive integer a & b, a is a positive integer. Hence, * is a binary operation on Z+.

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.