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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 (\mathbb{R}), (a*b=a+b+ab). Which form is most useful for explaining closure on (\mathbb{R}\setminus{-1})?Class 12Relations and FunctionsBinary operationsLevel 30Expert MathematicsOn (\mathbb{R}\setminus{0}), (a*b=\frac{a}{b}). Which statement is correct?Class 12Relations and FunctionsBinary operationsLevel 30Expert MathematicsOn (\mathbb{R}), (a*b=a-b). Which of the following statements is correct?Class 12Relations and FunctionsBinary operationsLevel 30Expert MathematicsOn (\mathbb{R}), (a*b=a+b-ab). Which element motivates restricting the operation to (\mathbb{R}\setminus{1})?Class 12Relations and FunctionsBinary operationsLevel 30Expert MathematicsOn (A=\mathbb{R}\setminus{-1}), (a*b=a+b+ab) is defined. Which statement about this operation is correct?Class 12Relations and FunctionsBinary operationsLevel 29Expert MathematicsOn (A=\mathbb{R}\setminus{1}), (a*b=a+b-ab) is defined. Choose the correct statement about this operation on this set.Class 12Relations and FunctionsBinary operationsLevel 29Expert MathematicsOn natural numbers, (a*b=a-b) is defined. Why is it not a binary operation?Class 12Relations and FunctionsBinary operationsLevel 29Expert MathematicsOn integers, (a*b=a+b+2ab) is defined. Is this a binary operation on integers?Class 12Relations and FunctionsBinary operationsLevel 29Expert MathematicsOn (A=\mathbb{R}-{1}), (a*b=a+b-ab). Why is it closed in (A)?Class 12Relations and FunctionsBinary operationsLevel 28Hard MathematicsOn (\mathbb{Z}), the operation (a*b=a+b+ab) is defined. Choose the correct statement.Class 12Relations and FunctionsBinary operationsLevel 28Hard MathematicsOn (A={1,2,4,5}), (a*b) is the remainder when (ab) is divided by (6). Which statement is correct?Class 12Relations and FunctionsBinary operationsLevel 28Expert MathematicsOn (\mathbb{Q}\setminus{0}), (a*b=\frac{a}{b}). In which property does this operation fail?Class 12Relations and FunctionsBinary operationsLevel 28Expert MathematicsOn (A={1,3,5,7}), (a*b) is the remainder when (a+b) is divided by (8). Is it closed on (A)?Class 12Relations and FunctionsBinary operationsLevel 28Expert MathematicsOn (A={x\in\mathbb{Z}:x\text{ is even}}), (a*b=\frac{a+b}{2}). Is it a binary operation?Class 12Relations and FunctionsBinary operationsLevel 28Expert MathematicsOn (\mathbb{Z}), (a*b=a+b+ab). Which option gives the best analysis for closure?Class 12Relations and FunctionsBinary operationsLevel 28Expert MathematicsOn (A=\mathbb{R}\setminus{1}), (a*b=a+b-ab). Which statement is correct?Class 12Relations and FunctionsBinary operationsLevel 28Expert MathematicsOn (A=\mathbb{R}\setminus{1}), (a*b=a+b-ab). Why is it closed on (A)?Class 12Relations and FunctionsBinary operationsLevel 30Hard MathematicsOn (\mathbb{R}), (a*b=a^2+b). Choose the correct statement.Class 12Relations and FunctionsBinary operationsLevel 30Hard MathematicsOn (\mathbb{R}), (a*b=a+b+ab). On which set will this operation not be closed?Class 12Relations and FunctionsBinary operationsLevel 30Hard MathematicsIf (a*b=a+b+2ab) is defined on (\mathbb{Z}), why is it a binary operation on (\mathbb{Z})?Class 12Relations and FunctionsBinary operationsLevel 30Hard