Let * be a binary operation on the set Q of rational numbers as follow

1.	Let * be a binary operation on the set Q of rational numbers as follows. Find which of the binary operations are commutative and which are associative. a * b = a – b
Answer» a * b = a – b,∀ a > be Q a * b = a – b * a = b – a a * b ≠ b * a hence not commutative (a * b) * c = (a – b) * c = a – b – c a* (b * c) = a* (b – c) = a – (b – c) = a – b + c ≠ (a* b) * c hence ≠ is not associative

Let * be a binary operation on the set Q of rational numbers as follows. Find which of the binary operations are commutative and which are associative. a * b = a – b

Answer»

a * b = a – b,∀ a > be Q

a * b = a – b * a = b – a

a * b ≠ b * a

hence not commutative

(a * b) * c = (a – b) * c

= a – b – c a* (b * c)

= a* (b – c) = a – (b – c)

= a – b + c ≠ (a* b) * c

hence ≠ is not associative