Join Sarthaks eConnect Today - Largest Online Education Community!
0 votes
3 views
in Sets, Relations and Functions by (51.8k points)
closed by

Define * on Z by a * b = a – b + ab. Show that * is a binary operation on Z which is neither commutative nor associative.

1 Answer

+1 vote
by (20.7k points)
selected by
 
Best answer

Commutative:

Consider two elements 1 and 2 of Z

Here, 1 * 2 = 1 – 2 + 1 × 2 = 1 and 2 * 1 = 2 – 1 + 2 × 1 = 3

Therefore, the operation is not commutative.

Associative:

Take 2, 3, 4 ∈ Z

We get

(2 * 3) * 4 = (2 – 3 + 2 × 3) * 4 = 5 * 4 = 5 – 4 + 5 × 4 = 21

2 * (3 * 4) = 2 * (3 – 4 + 12) = 2 * 11 = 2 – 11 + 2 × 11 = 13

Here, (2 * 3) * 4 ≠ 2 * (3 * 4)

Therefore, the operation is not associative.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...