Determine whether the operation define a binary operation or not: ′⋆′on N defined by a∗b=ab ∀ a,b∈N Watch Solution
Determine whether the operation define a binary operation or not:‘O’ on Z defined by aOb=ab ∀ a,b∈ Z Watch Solution
Determine whether the operation define a binary operation or not: on N defined by a*b=a+b-2 ∀ a,b∈ N Watch Solution
Determine whether the operation define a binary operation or not: ‘x6’ on S={1,2,3,4,5} defined by ax6b =Remainder when ab is divided by 6 Watch Solution
Determine whether the operation define a binary operation or not: +6′onS={0,1,2,3,4,5} defined by a+6b={a+b if a+b less than 6 ; a+b-6, if a+b≥6 Watch Solution
Determine whether the operation define a binary operation or not: ‘O’ on N defined by aOb=a^b+b^a ∀ a,b∈N Watch Solution
Determine whether the operation define a binary operation or not: ‘*’on Q defined by a∗b=(a-1)/(b+1) ∀ a,b∈Q Watch Solution
Determine whether or not definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On Z + , defined * by a*b = a – b Here, Z + denotes the set of all non-negative integers. Watch Solution
Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On Z + , defined * by a*b = ab Here, Z + denotes the set of all non-negative integers. Watch Solution
Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On R, defined * by a*b = ab^2 Here, Z + denotes the set of all non-negative integers. Watch Solution
Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On Z + , defined * by a*b = |a – b| Here, Z + denotes the set of all non-negative integers. Watch Solution
Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On Z + , defined * by a*b = a Here, Z + denotes the set of all non-negative integers. Watch Solution
Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On R, defined * by a*b = a + 4b^2 Here, Z + denotes the set of all non-negative integers. Watch Solution
Let * be a binary operation on the set I of integers, defined by a*b =2a+b-3. Find the value of 3*4. Watch Solution
Is * defined on the set {1,2,3,4,5} by a*b = LCM of a and b a binary operation? Justify your answer. Watch Solution
Let S = {a,b,c}. Find the total number of binary operations on S. Watch Solution
Find the total number of binary operations on {a, b} Watch Solution
Prove that the operation * on the set M = { [[a 0][0 b]] : a, b ∈ R – {0} } defined by A*B = AB is a binary operation. Watch Solution
Let S be the set of all rational numbers of the form m/n, where m∈Z and n = 1,2,3. Prove that * on S defined by a*b = ab is not a binary operation. Watch Solution
The binary operation * defined on R×R → R is defined as a*b = 2a + b. Find (2 * 3) * 4. Watch Solution
Let * be a binary operation on N given by a*b = LCM(a, b) for all a, b∈ N. Find 5 * 7. Watch Solution
