Let ‘*’ be a binary operation on N defined by a*b = L.C.M(a,b) for all a, b ∈N. Find (i) 2*4, 3*5, 1*6 (ii)Check the commutativity and associativity of ‘*’ on N. Watch Solution
Determine the binary operations are associative and which are commutative:* on N defined by a*b=1 ∀ a,b∈ N Watch Solution
Determine which of the following binary operations are associative and which are commutative:* on Q defined by a∗b = (a + b)/2 for all a, b∈ Q. Watch Solution
Let A be any set containing more than one element. Let ‘*’ be a binary operation on A defined by a*b = b for all a, b ∈A. Is ‘*’ commutative or associative on A ? Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on Z defined by a*b = a + b + ab ∀ a, b ∈Z Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on N defined by a*b = 2^ab ∀ a, b ∈N Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on Q defined by a*b = a – b for all a, b ∈Q Watch Solution
Check the commutativity and associativity of the binary operations:‘Ο’ on Q defined by aΟb = a^2 + b^2 for all a, b ∈Q Watch Solution
Check the commutativity and associativity of the binary operations: ‘o’ on Q defined by a o b = ab/2 for all a, b ∈ Q Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on Q defined by a*b = ab^2 for all a,b∈Q Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on Q defined by a*b = a + ab for all a, b ∈Q. Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on R defined by a*b = a + b – 7 ∀ a, b ∈R. Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on Q defined by a*b=(a-b)^2 ∀ a, b ∈Q. Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on Q defined by a*b = ab + 1 ∀ a, b ∈Q Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on N defined by a⋅b = a^b ∀ a, b ∈ N Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on Z defined by a*b=a-b ∀ a, b ∈Z Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on Q defined by a*b = ab/4 ∀ a, b ∈Q Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on Z defined by a*b = a + b-ab ∀ a, b ∈Z Watch Solution
Check the commutativity and associativity of the binary operations:‘*’ on Q defined by a*b = gcd(a, b) ∀ a, b ∈Q Watch Solution
If the binary operation ο is defined by aοb = a + b – ab on the set Q – { -1} of all rational numbers other than -1. Show that ο is commutative on Q – { – 1}. Watch Solution
Show that the binary operation * on Z defined by a*b = 3a + 7b is not commutative. Watch Solution
On the set Z of integers a binary operation * is defined by a*b = ab + 1 for all a, b ∈Z. Prove that * is not associative on Z. Watch Solution
Let S be the set of all real numbers except – 1 and let ‘*’ be an operation defined by a*b = a + b + ab for all a, b ∈S. Determine whether ‘*’ is a binary operation on ‘S’. if yes, Check its commutativity and associativity. Also, solve the equation (2*x)*3 = 7. Watch Solution
On Q, the set of all rational numbers, * is defined by a∗b = (a-b)/2 show that * is not associative. Watch Solution
On Z, the set of all integers, a binary operation * is defined by a*b = a + 3b – 4. Prove that * is neither commutative nor associative on Z. Watch Solution
On the set Q of all rational numbers if a binary operation * is defined by a∗b=ab/5, prove that * is associative on Q. Watch Solution
The binary operation * is defined by a∗b=ab/7 on the set Q if all rational numbers. Show that * is associative. Watch Solution
On Q, the set of all rational numbers a binary operation * is defined by a∗b = (a+b)/2. Show that * is not associative on Q. Watch Solution
Let S be the set of all rational numbers except 1 and * be defined on S by a*b = a + b – ab, for all a, b ∈S. Prove that: i. * is a binary operation on S ii. * is commutative as well as associative. Watch Solution
