Question
Construct the composition table for $\times _4$ on set $S = {0, 1, 2, 3}$.
✓
Answer
Here,
$1\times _41$ = Remainder obtained by dividing $1 \times 1$ by $4 = 1$
$0\times _41$ = Remainder obtained by dividing $0 \times 1$ by $4 = 0$
$2\times _43$ = Remainder obtained by dividing $2 \times 3$ by $4 = 2$
$3\times _43$ = Remainder obtained by dividing $3 \times 3$ by $4 = 1$
Therefore,
The composition table is as follows:
$1\times _41$ = Remainder obtained by dividing $1 \times 1$ by $4 = 1$
$0\times _41$ = Remainder obtained by dividing $0 \times 1$ by $4 = 0$
$2\times _43$ = Remainder obtained by dividing $2 \times 3$ by $4 = 2$
$3\times _43$ = Remainder obtained by dividing $3 \times 3$ by $4 = 1$
Therefore,
The composition table is as follows:
| $x_4$ | 0 | 1 | 2 | 3 |
| 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 2 | 3 |
| 2 | 0 | 2 | 0 | 2 |
| 3 | 0 | 3 | 2 | 1 |
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Evaluate the following integrals:
$\int\text{x e}^{\text{x}^2}=\text{dx}$
→$\int\text{x e}^{\text{x}^2}=\text{dx}$
Find the Cartesian equations of the line which passes through the point (-2, 4, -5) and
→parallel to the line $\frac{x+2}{3}=\frac{y-3}{5}=\frac{z+5}{6}$
If $x = a \cos ^3 t , y = a \sin ^3 t$, then show that $\frac{d y}{d x}=-\left(\frac{y}{x}\right)^{\frac{1}{3}}$
→Write the symbolic form of the following switching circuits construct its switching table and interpret it.
If $\text{y}=\cos^{-1}(2\text{x})+2\cos^{-1}\sqrt{1-4\text{x}^2}, 0 <\text{x}<\frac{1}{2},$ find $\frac{\text{dy}}{\text{dx}}.$
→Evaluate: $\sin^{-1}\Big(\sin\frac{3\pi}{5}\Big).$
→Construct the simplified circuit for the following circuit.
A card is drawn from a well-shuffled deck of 52 cards and then a second card is drawn. Find the probability that the first card is a heart and the second card is a diamond if the first card is not replaced.
If $\text{y}=\log(\sin\text{x})$ Prove that $\frac{\text{d}^3\text{y}}{\text{dx}^3}=2\cos\text{x}\ \text{cosec}^3\text{x}$
→Solve the following differential equations:
→$\cos ^2 x \cdot \frac{d y}{d x}+ y =\tan x$