Mathematics
Binary operations
द्विआधारी संक्रियाएँ
In Class 12 Mathematics, this topic introduces binary operations as functions that combine two elements of a set to produce another element of the same set. Within the chapter Relations and Functions, students learn to identify whether an operation is well-defined and closed, represent it through tables or algebraic rules, and examine key properties such as commutativity, associativity, identity elements, and inverses. Examples involving familiar number systems help connect these ideas with broader function concepts.
Practice questions
On (A={-1,0,1}), (a*b=a+b-ab) is defined. Is it a binary operation on (A)?On real numbers, (a*b=a+b+ab) is defined. Choose the correct statement about this operation.In the operation (a*b=a+b+ab) on real numbers, which element does not have an inverse?On real numbers, (a*b=a+b-2ab) is defined. What is the inverse of (3)?In the operation (a*b=a+b-2ab) on real numbers, which element will not have an inverse?On real numbers, \(a*b=a+b+k ab\) is defined. If the inverse of (2) is \(-\frac{1}{2}\), what is the value of (k)?On the set (A=\mathbb{R}\setminus{1}), the operation (a*b=a+b-ab) is given. Which element is the identity for this operation?On (A=\mathbb{R}\setminus{1}), (a*b=a+b-ab). What is the inverse of (a)?On positive real numbers, (a*b=\frac{ab}{2}). Which is the inverse of (a)?On integers, (a*b=a+b+ab) is given. Is this operation closed on integers?On integers, (a*b=a+b+ab). Which is the identity element of this operation?On integers, (a*b=a+b+ab). For which (a) will inverses exist in integers under this operation?On (A={1,2,3,4}), (a*b=\min(a,b)). Which is the identity element?On (A={1,2,3,4}), (a*b=\max(a,b)). What is the identity element?On real numbers, (a*b=a+b+2). Which is the inverse of (a) under this operation?On real numbers, (a*b=a+b+2). What type of operation is it?On real numbers, (a*b=a+b+ab). Which statement is correct?On natural numbers, (a*b=a^b). Which property does this operation not satisfy?On natural numbers, (a*b=a^b). Which statement is correct?On real numbers, (a*b=a-b). Choose the correct statement about this operation.