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
If the operation (a*b) on (S={0,1,2,3}) is defined as the remainder when (a+b) is divided by (4), then is this operation closed on (S)?On real numbers, (a*b=a+b+2). What is the identity element of this operation?On integers, (a*b=a+b-3). What is the inverse element of (5)?On real numbers, (a*b=a+b+ab). Which is the identity element for this operation?If (a*b=a+b+ab), under what result condition do we find the inverse of (2)?On (A={1,2,3}), (a*b=\max(a,b)). What is the identity element of this operation?On (A={1,2,3}), (a*b=\min(a,b)). What is the identity element of this operation?On real numbers, (a*b=a-b). Is this operation commutative?On real numbers, (a*b=a+b+ab). Is this operation commutative?On integers, (a*b=a+b+1). Is this operation associative?On real numbers, (a*b=a+b+ab). Is this operation associative?On positive real numbers, (a*b=\frac{ab}{2}). What is the identity element?On positive real numbers, (a*b=\frac{ab}{2}). What is the inverse of (6)?On integers, (a*b=a+b+ab). Which statement is correct about the inverse of (-1)?On (A={0,1}), (a*b=a+b-ab). What is the value of (1*1)?On (A={0,1}), (a*b=a+b-ab). What is the identity element?On real numbers, (a*b=a^2+b^2). Is this operation associative?On integers, (a*b=a+2b). Is this operation commutative?On real numbers, (a*b=a+b-ab). Which is the identity element of this operation?On real numbers, (a*b=a+b-ab). What is the inverse of (2)?