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={0,1,2,3}), (a*b) is the remainder obtained when (a+b) is divided by (4). What is the inverse of (3)?On real numbers, (a*b=a+b-ab) is defined. What is the identity element?On real numbers, (a*b=a+b-ab) is defined. For (a\neq1), what is the inverse of (a)?On natural numbers, (a*b=a+b) is defined. Is this a binary operation?On natural numbers, (a*b=a-b) is defined. Is this a binary operation?On integers, (a*b=ab+1) is defined. Is this operation commutative?On integers, (a*b=ab+1) is defined. Is this operation associative?On real numbers, (a*b=\frac{a+b}{2}) is defined. Which property does this operation have?On real numbers, (a*b=a+b+ab) is defined. What is the inverse of (2)?On real numbers, (a*b=a+b+ab) is defined. Which element does not have an inverse under this operation?On (A={1,2,3,4}), (a*b=a) is defined. Which statement is correct?On (A={1,2,3}), (a*b=b) is defined. Which statement is correct?On real numbers, (a*b=a+b-3) is defined. What is the identity element?On real numbers, (a*b=a+b-3) is defined. What is the inverse of (5)?For (a*b=a+b+ab) on real numbers, what is the value of (1*2)?If (a*b=2a+b), what is the value of ((1*2)*3)?On real numbers, (a*b=a+2b) is defined. Is this operation associative?On real numbers, (a*b=a+b-ab) is defined. Choose the correct statement for this operation.On real numbers, (a*b=a+b-4) is defined. What will be the inverse of (7)?On (A={1,2,3,4,6,12}), (a*b) is the least common multiple of (a) and (b). What is the identity element?