Ex 1.4 ,1 - Chapter 1 Class 12 Relation and Functions
Last updated at Jan. 28, 2020 by Teachoo
Last updated at Jan. 28, 2020 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 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. (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+.
Ex 1.4
Ex 1.4, 2 Important Deleted for CBSE Board 2021 Exams only
Ex 1.4, 3 Deleted for CBSE Board 2021 Exams only
Ex 1.4, 4 Deleted for CBSE Board 2021 Exams only
Ex 1.4, 5 Deleted for CBSE Board 2021 Exams only
Ex 1.4, 6 Deleted for CBSE Board 2021 Exams only
Ex 1.4, 7 Deleted for CBSE Board 2021 Exams only
Ex 1.4, 8 Deleted for CBSE Board 2021 Exams only
Ex 1.4, 9 Deleted for CBSE Board 2021 Exams only
Ex 1.4, 10 Deleted for CBSE Board 2021 Exams only
Ex 1.4, 11 Important Deleted for CBSE Board 2021 Exams only
Ex 1.4, 12 Deleted for CBSE Board 2021 Exams only
Ex 1.4, 13 Deleted for CBSE Board 2021 Exams only
Ex 1.4
About the Author