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 every entry in the table of a binary operation belongs to the same set, what does it indicate?If an operation table contains an element outside the set (A), what conclusion follows?If set (A) has (2) elements, how many binary operations are possible on (A)?If set (A) has (3) elements, what is the number of binary operations on (A)?Why is (a*b=\frac{a+b}{2}) not a binary operation on integers?On rational numbers, what type is (a*b=\frac{a+b}{2})?For real numbers, which statement is correct about (a*b=a^2+b^2)?Why is (a*b=a^2+b^2) commutative on real numbers?On real numbers, what is the identity element for (a*b=a+b+2)?Under (a*b=a+b+2) on real numbers, what is the inverse of (3)?On the set (A={1,2,3}), an operation (\ast) is defined by (a\ast b=a). Is it a binary operation?On the set of natural numbers (N), the operation (a\ast b=a-b) is given. Is it a binary operation on (N)?On the set of integers (Z), the operation (a\ast b=a+b+1) is given. Which statement is correct?On the set of real numbers (R), the operation (a\ast b=ab) is given. What is the identity element?For the operation (a\ast b=a+b) on real numbers, what is the inverse of (5)?On the set (A={0,1}), the operation (\ast) is defined by (a\ast b=ab). What is the inverse of (1) under this operation?If (a\ast b=a+b-2) is defined on real numbers, find the identity element.If (a\ast b=a+b+ab), what is the value of (0\ast 5)?For the operation (a\ast b=a+2b), find the value of (3\ast 4).If (a\ast b=2a+b), is the operation commutative?