Download App

Binary Operations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsBinary Operations3 Marks
Question
Let $+_6 ($addition modulo $6) $ be a binary operation on $S = \{0, 1, 2, 3, 4, 5\}$. Write the value of $2 + _64^{−1}+ _63^{−1}.$
✓

Answer

The composition table for $+_6$ on the set $S = \{0, 1, 2, 3, 4, 5\}$ is
$+_6$ $0$ $1$ $2$ $3$ $4$ $5$
$0$ $0$ $1$ $2$ $3$ $4$ $5$
$1$ $1$ $2$ $3$ $4$ $5$ $0$
$2$ $2$ $3$ $4$ $5$ $0$ $1$
$3$ $3$ $4$ $5$ $0$ $1$ $2$
$4$ $4$ $5$ $0$ $1$ $2$ $3$
$5$ $5$ $0$ $1$ $2$ $3$ $4$
$'0' $ is the identity element for $+_6$ from the table it is clear that
$4^{-1} = 2$ and $3^{-1} = 3$
Now, $2 + _64^{-1} + _63^{-1} = 2 + _62 + _63$
$= 4 + _63$
$= 1$

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

Explore more

More "3 Marks Question" from Binary Operations→Binary Operations — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\log(\text{x}+1)\text{dx}$
→
Find gof and fog when f : R → R and g : R → R are defined by:
f(x) = x and g(x) = |x|
→
If $\vec{\text{a}}=2\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}},\vec{\text{b}}=-\hat{\text{i}}+2\hat{\text{j}}+\hat{\text{k}},$and $\vec{\text{c}}=3\hat{\text{i}}+\hat{\text{j}}$ are such that $\vec{\text{a}}+\lambda\vec{\text{b}}$ is perpendicular to $\vec{\text{c}},$ then find the value of $\lambda.$
→
Write the interval in which $\text{f}(\text{x})=\sin\text{x}+\cos\text{x},\text{x}\in\Big[0,\frac{\pi}{2}\Big]$ is increasing.
→
Differentiate w.r.t. x the function in Exercise:
$(5\text{x})^{3\cos2\text{x}}$
→
If f(x) = |x|, prove that fof = f.
→
Differentiate the following functions with respect to x:
$\log_7(2\text{x}-3)$
→
Using differentials, find the approximate value of each of the following up to 3 places of decimal.
$(3.968)^{\frac{3}{2}}$
→
Discuss the continuity of the function f(x) at the point x = 0, where$\text{f}\text{(x)}=\begin{cases}\text{x}, & \text{x} > 0\\1,&\text{x}=0\\\text{-x}, & \text{x} > 0\end{cases}$
→
Write the value of b which $\text{f(x)}=\begin{cases}5\text{x}-4,&0<\text{x}\leq1\\4\text{x}^2+3\text{bx},&1<\text{x}<2\end{cases}$ is continuous at x = 1.
→