If the binary operation * on the set Z is defined by a * b = a + … - Vidyadip

Question

If the binary operation * on the set Z is defined by a * b = a + b - 5, the find the identity element with respect to *.

✓

Answer

Let e be the identity element in Z with respect to * such that,
a * e = a = e * a, $\forall\ \text{a}\in\text{Z}$
a * e = a and e * a = a, $\forall\ \text{a}\in\text{Z}$
a + e - 5 = a and e + a - 5 = a, $\forall\ \text{a}\in\text{Z}$
e = 5, $\forall\ \text{a}\in\text{Z}$
Thus, 5 is the identity element in Z with respect to *.

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 "2 Marks" 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

If |x| < 1 and $\text{y}=1+\text{x}+\text{x}^2+\ .....\ \text{to}\ \infty,$ then find the value of $\frac{\text{dy}}{\text{dx}}.$

For any two vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ write the value of $\big(\vec{\text{a}}.\vec{\text{b}}\big)^2+\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2$ in terms of their magnitudes.

If x and y are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.$
x = 2at², y = at⁴

If a vector makes angles $\alpha,\beta,\gamma$ with OX, OY and OZ respectively. then write the value of $\sin^2\alpha+\sin^2\beta+\sin^2\gamma$.

Find the general solution of the differential equation $\left(1+x^2\right) d y=\left(1+y^2\right) d x$.

Write the equation of the plane parallel to the YOZ- plane and passing through (-4, 1, 0).

Find the area of the region bounded by the ellipse $9 x^2+16 y^2=144$.

Evaluate the following integrals:
$\int\frac{1}{1-\cos2\text{x}}\text{dx}$

Evaluate the following integral:
$\int\frac{1}{\text{a}^2\text{x}^2-\text{b}^2}\text{ dx}$

Write the direction cosines of the vectors $-2\hat{\text{i}}+\hat{\text{j}}-5\hat{\text{k}}$.