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Class 12 · Mathematics
→On (A=\mathbb{R}^{+}), (a*b=\frac{a+b}{2}). What is true about the identity element?
Class 12 · Mathematics
→On (A=\mathbb{R}^{+}), (a*b=ab). In which set does the inverse of (a) lie?
Class 12 · Mathematics
→On (\mathbb{R}), (a*b=a+b+ab). Which condition is necessary and sufficient for (a*b=b)?
Class 12 · Mathematics
→On (A={1,-1}), ordinary multiplication is the operation. What is the correct statement about this structure?
Class 12 · Mathematics
→On (A={0,1}), the operation (a*b) is ordinary multiplication. Which element has no inverse?
Class 12 · Mathematics
→On (\mathbb{Q}\setminus{0}), (a*b=\frac{a}{b}). Is this operation associative?
Class 12 · Mathematics
→On (\mathbb{Q}\setminus{0}), (a*b=\frac{a}{b}). In which property does this operation fail?
Class 12 · Mathematics
→On (\mathbb{R}), (a*b=a+b-ab). When will (a*b=1)?
Class 12 · Mathematics
→On (\mathbb{R}), (a*b=2a+b). Does this operation have an identity element?
Class 12 · Mathematics
→On (\mathbb{R}), (a*b=a+2b). Choose the correct statement.
Class 12 · Mathematics
→On (\mathbb{R}\setminus{-\frac{1}{2}}), (a*b=a+b+2ab). What is the inverse of (a)?
Class 12 · Mathematics
→On (\mathbb{R}\setminus{-\frac{1}{k}}), (a*b=a+b+kab), where (k\neq 0). What is the identity element?
Class 12 · Mathematics
→On (\mathbb{R}), (a*b=a+b+kab). For which values of (k) is the operation associative?
Class 12 · Mathematics
→On (\mathbb{R}), (a*b=a^2+b^2). Is this operation associative?
Class 12 · Mathematics
→On (\mathbb{R}), (a*b=a^2+b^2). Why is this operation commutative?
Class 12 · Mathematics
→On (A={1,3,5,7}), (a*b) is the remainder when (a+b) is divided by (8). Is it closed on (A)?
Class 12 · Mathematics
→On (A={x\in\mathbb{Z}:x\text{ is even}}), (a*b=\frac{a+b}{2}). Is it a binary operation?
Class 12 · Mathematics
→On (\mathbb{Z}), (a*b=a+b+ab). Which option gives the best analysis for closure?
Class 12 · Mathematics
→On (A=\mathbb{R}\setminus{1}), (a*b=a+b-ab). Which statement is correct?
Class 12 · Mathematics
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