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Class 12 · Mathematics

On real numbers, (a*b=ab+1). Does it have an identity element?

Class 12 · Mathematics

On real numbers, (a*b=a+b+ab). Which is the identity element of this operation?

Class 12 · Mathematics

On real numbers, (a*b=a+b+1). What is the identity element of this operation?

Class 12 · Mathematics

If (a*b=a-b) is defined on real numbers, which statement is correct?

Class 12 · Mathematics

If (a*b=a+b) is defined on real numbers, what type of operation is it?

Class 12 · Mathematics

Why is usual division (\div) not a binary operation on the set of integers (\mathbb{Z})?

Class 12 · Mathematics

How is usual multiplication (\times) on the set of integers (\mathbb{Z})?

Class 12 · Mathematics

Why is usual subtraction (-) not a binary operation on the set of natural numbers (\mathbb{N})?

Class 12 · Mathematics

Why is usual addition (+) a binary operation on the set of natural numbers (\mathbb{N})?

Class 12 · Mathematics

If (a,b\in A) implies (a*b\in A), which property does this show?

Class 12 · Mathematics

What is the correct meaning of a binary operation on a set (A)?

Class 12 · Mathematics

Let (f:\mathbb{R}\to\mathbb{R}), where (f(x)=x^3-6x^2+12x-5). Choose the correct statement about (f) being onto.

Class 12 · Mathematics

If (f:A\to B) is onto and (b) is an element of (B), which is the best explanation of onto behavior?

Class 12 · Mathematics

Is (f:\mathbb{R}\to[0,1)), where (f(x)=\frac{x^2}{1+x^2}), onto?

Class 12 · Mathematics

If (f:\mathbb{R}\to\mathbb{R}), where (f(x)=\frac{x^2}{1+x^2}), why is (f) not onto?

Class 12 · Mathematics

Let (f:\mathbb{R}\to\mathbb{Z}), where (f(x)=\lceil x\rceil). Choose the correct statement for (f).

Class 12 · Mathematics

If (f:\mathbb{R}\to\mathbb{Z}), where (f(x)=\lfloor x\rfloor), is (f) onto?

Class 12 · Mathematics

Is (f:\mathbb{R}\to\mathbb{R}), where (f(x)=\lfloor x\rfloor), onto or not?

Class 12 · Mathematics

If (f:[0,2]\to[0,4]), where (f(x)=x^2), what type is (f)?

Class 12 · Mathematics

Let (f:[-2,2]\to[0,4]), where (f(x)=x^2). Which statement is correct about (f)?