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
What is the identity element for usual addition on real numbers?What is the inverse of (7) under usual addition?What is the inverse of (5) under usual multiplication?On the set ({1,2,3}), (a*b=\min(a,b)). What is the identity element?On the set ({1,2,3}), (a*b=\max(a,b)). What is the identity element?On the set (\mathbb{Q}), (a*b=a+b) is defined. Why is it a binary operation?Why can (a*b=\sqrt{a+b}) not be considered a binary operation on (\mathbb{N})?On the set of integers (\mathbb{Z}), what type is (a*b=|a-b|)?Why is usual multiplication a binary operation on the set ({0,1})?Why is usual addition not a binary operation on the set ({0,1})?On the set ({0,1}), (a*b) is the remainder obtained when (a+b) is divided by (2). What is the identity element?On the set ({0,1}), (a*b) is the remainder of (a+b) on division by (2). What is the inverse of (1)?On the set ({0,1,2}), (a*b) is the remainder of (a+b) on division by (3). Which is the identity element?On the set ({0,1,2}), (a*b) is the remainder of (a+b) on division by (3). Which is the inverse of (2)?If (a*b=b*a) is true for every (a,b) in a binary operation, what is the operation called?If ((a*b)*c=a*(b*c)) is true for every (a,b,c), which property is it?If (e) is an element such that (a*e=e*a=a) for every (a), what is (e) called?If (a*b=e) and (b*a=e), where (e) is the identity element, what is (b) called for (a)?On the set (A={1,2}), (a*b=a) is defined. Is it commutative?On the set (A={1,2}), (a*b=b) is defined. What is the value of (1*2)?