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 positive real numbers, (a\ast b=\frac{ab}{2}) is given. What is the identity element?On real numbers, (a\ast b=\frac{a+b}{2}) is given. Does it have an identity element?The operation (a\ast b=a^2+b^2) is given on real numbers. Is it a binary operation on (R)?On integers, the operation (a\ast b=\frac{a+b}{2}) is given. Is it a binary operation on (Z)?On the set of even integers, (a\ast b=a+b) is given. Is it a binary operation?On the set of odd integers, (a\ast b=a+b) is given. Is it a binary operation?On the set of even integers, (a\ast b=ab) is given. Is it a binary operation?On the set of odd integers, (a\ast b=ab) is given. Is it a binary operation?On the set of non-zero real numbers, (a\ast b=\frac{a}{b}) is given. Is it a binary operation?On the set of real numbers (R), (a\ast b=\frac{a}{b}) is given. Is it a binary operation?The operation (a\ast b=a) is given on a set (A). What is the nature of this operation?The operation (a\ast b=b) is given on a set (A). What will be the value of (x\ast y)?If (a\ast b=a+b-5), what is the value of (7\ast 3)?If (a\ast b=a+b-5), what is the identity element of this operation?If (a\ast b=a+b-5), what is the inverse of (2)?The operation (a\ast b=2ab) is given on non-zero real numbers. What is the identity element?In the operation (a\ast b=2ab), (\frac{1}{2}) is the identity. What is the inverse of (4)?In the operation (a\ast b=2ab), what is the inverse of (4)?If (a\ast b=a+b+1), what is the value of (2\ast(3\ast4))?If (a\ast b=a+b+1), what is the value of ((2\ast3)\ast4)?