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Last updated at Jan. 28, 2020 by Teachoo
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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 Not in Syllabus - CBSE Exams 2021
Ex 1.4, 3 Not in Syllabus - CBSE Exams 2021
Ex 1.4, 4 Not in Syllabus - CBSE Exams 2021
Ex 1.4, 5 Not in Syllabus - CBSE Exams 2021
Ex 1.4, 6 Not in Syllabus - CBSE Exams 2021
Ex 1.4, 7 Not in Syllabus - CBSE Exams 2021
Ex 1.4, 8 Not in Syllabus - CBSE Exams 2021
Ex 1.4, 9 Not in Syllabus - CBSE Exams 2021
Ex 1.4, 10 Not in Syllabus - CBSE Exams 2021
Ex 1.4, 11 Important Not in Syllabus - CBSE Exams 2021
Ex 1.4, 12 Not in Syllabus - CBSE Exams 2021
Ex 1.4, 13 Not in Syllabus - CBSE Exams 2021
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