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Closure

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsOn (A=\mathbb{R}\setminus{1}), (a*b=a+b-ab). Why is this operation closed in (A)?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn natural numbers, (a*b=a+b-2). When does this operation fail to be closed on natural numbers?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn (A=\mathbb{R}\setminus{0}), (a*b=\frac{ab}{2}). Which statement is correct?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn (A={1,2,3,4}), (a*b) is the remainder when (ab) is divided by (5), and remainder (0) is not replaced by (5). Is this a binary operation on (A)?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn (A=\mathbb{Q}\setminus{0}), (a*b=\frac{a}{b}). Is it a binary operation?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn (A=\mathbb{R}\setminus{-1}), (a*b=a+b+ab). Why is this operation closed in (A)?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn (\mathbb{R}\setminus{0}), (a*b=\frac{ab}{a+b}), where (a+b\neq0). Why is it not a binary operation on the whole set?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn integers, (a*b=a+b+ab) is given. Is this operation closed on integers?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn (A={-1,0,1}), (a*b=a+b-ab) is defined. Is it a binary operation on (A)?Class 12Relations and FunctionsBinary operationsLevel 28Hard MathematicsOn (A={1,2,3,4}), (a*b=|a-b|) is defined. Is this a binary operation?Class 12Relations and FunctionsBinary operationsLevel 30Medium MathematicsOn natural numbers, (a*b=\frac{a+b}{2}) is defined. Is this a binary operation?Class 12Relations and FunctionsBinary operationsLevel 30Medium MathematicsOn integers, (a*b=a+b+ab) is defined. Is this operation closed on integers?Class 12Relations and FunctionsBinary operationsLevel 30Medium MathematicsOn natural numbers, (a*b=a-b) is defined. Is this a binary operation?Class 12Relations and FunctionsBinary operationsLevel 30Medium MathematicsOn natural numbers, (a*b=a+b) is defined. Is this a binary operation?Class 12Relations and FunctionsBinary operationsLevel 30Medium MathematicsOn (A={1,2,3,4}), (a*b=\min(a+b,4)). Is this operation closed on (A)?Class 12Relations and FunctionsBinary operationsLevel 29Medium MathematicsOn integers, (a*b=a^2+b^2). Is this operation closed?Class 12Relations and FunctionsBinary operationsLevel 29Medium MathematicsOn natural numbers, (a*b=a-b). Is this operation closed on natural numbers?Class 12Relations and FunctionsBinary operationsLevel 29Medium MathematicsOn natural numbers, (a*b=a+b). Is this operation closed on natural numbers?Class 12Relations and FunctionsBinary operationsLevel 29Medium MathematicsIf the operation (a*b) on (S={0,1,2,3}) is defined as the remainder when (a+b) is divided by (4), then is this operation closed on (S)?Class 12Relations and FunctionsBinary operationsLevel 29Medium MathematicsIf (a*b=a-b) is taken on the set of multiples of (5), what is the correct statement about closure?Class 12Relations and FunctionsBinary operationsLevel 28Medium