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 (\mathbb{R}\setminus{-1}), (a*b=a+b+ab) is given. This operation is related to which expression?If (a*b=a+b-ab), then (1-a*b) is equal to what?On (\mathbb{R}), (a*b=a+b-ab). Which element has no inverse?If (a*b=a+b-2ab), what is the identity element of this operation?On (\mathbb{R}), (a*b=a+b-2ab). Which element will not have an inverse?On (\mathbb{R}), (a*b=a+b-2ab). What is the inverse of (2)?On (\mathbb{Z}), (a*b=a+b+ab). Is it associative on (\mathbb{Z})?On (A={1,2,3,4}), (a*b=\min(a+b,4)). What is true about the identity element?On (A={0,1,2,3}), (a*b) is the remainder when (a+b) is divided by (4). What is the inverse of (3)?On (A={0,1,2,3}), (a*b) is the remainder when (ab) is divided by (4). Which element has a multiplicative inverse?On (\mathbb{R}), (a*b=a^2+b). Choose the correct statement.On (\mathbb{R}), (a*b=a^2+b). What prevents (0) from being an identity?If (a*b=a+b+kab) and (k\neq0), which element will not have an inverse?On (\mathbb{R}), (a*b=a+b+3ab). What is the inverse of (2)?On (\mathbb{R}), (a*b=a+b+3ab). Which element has no inverse?On (\mathbb{R}), (a*b=a+b-ab). For (a*b=0), what is (b) equal to?On (\mathbb{R}), (a*b=a+b-ab). Is this operation commutative?On (\mathbb{R}), (a*b=a+b-ab). Is it associative?On (A=\mathbb{R}\setminus{1}), (a*b=a+b-ab). Why is it closed on (A)?On (\mathbb{R}\setminus{1}), (a*b=a+b-ab). What is the inverse of (3)?