Question
The binary operation × defined on N by a × b = a + b + ab for all a, b ∈ N is:
  1. Commutative only.
  2. Associative only.
  3. Both commutative and associative.
  4. None of these.

Answer

  1. Both commutative and associative.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A die is thrown three times. Getting a $3$ or a $6$ is considered success. Then the probability of at least two successes is
If $p, q, r$ are $3$ real numbers satisfying the matrix equation, $[p\,q\,r]\,\left[ {\begin{array}{*{20}{c}}
3&4&1\\
3&2&3\\
2&0&2
\end{array}} \right] = [3\,\,\,0\,\,\,1]$ then $2p + q - r$ equals
A linear programming problem (LPP) along with the graph of its constraints is shown below. The corresponding objective function is
Minimize: $Z=3 x+2 y$. The minimum value of the objective function is obtained at the corner point ( 2 , 0).
The optimal solution of the above linear programming problem $\qquad$
Image
The diagram given below shows that
Image
The order of the differential equation whose solution is $y = a\cos x + b\sin x + c{e^{ - x}}$ is
Let $\omega$ be a complex cube root of unity with $\omega \neq 1$ and $P=\left[p_j\right]$ be a $n \times n$ matrix with $p_{i j}=\omega^{i+j}$. Then $P ^2 \neq 0$, when $n =$

$(A)$ $57$ $(B)$ $55$ $(C)$ $58$ $(D)$ $56$

$\int\frac{1}{7}\sin\Big(\frac{\text{x}}{7}+10\Big)\text{dx}$ is equal to:
  1. $\frac{1}{7}\cos\Big(\frac{\text{x}}{7}+10\Big)\text{C}$
  2. $-\frac{1}{7}\cos\Big(\frac{\text{x}}{7}+10\Big)\text{C}$
  3. $\cos\Big(\frac{\text{x}}{7}+10\Big)\text{C}$
  4. $-7\cos\Big(\frac{\text{x}}{7}+10\Big)\text{C}$
  5. $\cos(\text{x}+70)+\text{C}$
Range of $f(x) = sin^{-1} (\sqrt {x^2 + x +1})$ is -
If $f\left( x \right) = {\sin ^{ - 1}}\left( {\frac{{2 \times {3^x}}}{{1 + {9^x}}}} \right)$, then $f'(-\frac {1}{2})$ equals
If vector $\vec{a}$=2 \hat{i}+5 \hat{j}$ and $b=2 \hat{i}-\hat{j}$ then unit vector in the direction of the vector $\vec{a}$+$\vec{b}$ is :