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
The operation (a\ast b=a+b+3) is given on real numbers. What type of operation is it?The operation (a\ast b=a-b) is given on integers. Is it commutative?On real numbers, (a\ast b=ab+1) is given. Is it commutative?For the operation (a\ast b=a+2b), what are (2\ast 3) and (3\ast 2), respectively?If (a\ast b=a+b-1), what is the identity element of this operation?If (a\ast b=a+b+ab), what is the identity element of this operation?In the operation (a\ast b=a+b+2), find the inverse of (3).In the operation (a\ast b=a+b+2), what is the inverse of (3)?On the set (A={1,2,3,4}), (a\ast b=\min(a,b)) is given. What is (3\ast 4)?On the set (A={1,2,3,4}), (a\ast b=\max(a,b)) is given. What is the identity element of this operation?On (A={1,2,3,4}), (a\ast b=\min(a,b)). What is the identity element of this operation?For the operation (a\ast b=a+b) on integers, which statement is correct?For the operation (a\ast b=a-b) on integers, which statement is correct?The operation (a\ast b=ab) is given on real numbers. What is its nature?If (a\ast b=a+b+ab), find the value of (1\ast 2).If (a\ast b=a+b-ab), what is (0) for this operation?On the set (A={0,1,2}), (a\ast b) is defined as the remainder when (a+b) is divided by (3). What is (2\ast 2)?On (A={0,1,2}), (a\ast b) is the remainder of (a+b) upon division by (3). What is the identity element?On (A={0,1,2}), (a\ast b) is the remainder of (a+b) upon division by (3). What is the inverse of (1)?On (A={0,1,2,3}), (a\ast b) is the remainder of (a+b) upon division by (4). What is (3\ast 3)?