For any two sets A and B, prove the following: A (A' )=A - Vidyadip

Question

For any two sets A and B, prove the following:
$\text{A}\cap\text{(A}'\cup\text{B})=\text{A}\cap\text{B}$

✓

Answer

$\text{LHS}=\text{A}\cap\text{(A}'\cup\text{B)}$
$=\text{(A}\cap\text{A}')\cup\text{(A}\cap\text{B)}$ $[\because\cap$ distributes over (i)$]$
$= \oint\cup\text{ (A}\cap\text{B)}$ $[\because\text{A}\cap\text{A}' = \oint]$
$=\text{A}\cap\text{B}$ $[\because\oint\cup$ x = x for any set x$]$
$= \text{RHS}$
$\therefore$ LHS = RHS Proved.

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 "(Each question 4 marks)" from Sets→Sets — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Find $\lim\limits_{\text{x}\rightarrow0}\text{f}(\text{x})$, where $\text{f}(\text{x})\begin{cases}\frac{|\text{x}|}{\text{x}}, &\text{x}\neq 0\\0, & x > 0\end{cases}$

If $\frac{\text{b}+\text{c}}{\text{a}},\ \frac{\text{c}+\text{a}}{\text{b}},\ \frac{\text{a}+\text{b}}{b}$ are A.P., prove that: $\frac{1}{\text{a}},\ \frac{1}{\text{b}},\ \frac{1}{\text{c}}$ are in A.P.

Prove that the coefficient of $x^n$ in the expansion of $(1+x)^{2 n}$ is twice the coefficient of $x^n$ in the expansion of $(1+x)^{2 n-1}$.

$\text{a}\sin\frac{\text{A}}{2}\sin\Big(\frac{\text{B}-\text{C}}{2}\Big)+\text{b}\sin\frac{\text{B}}{2}\sin\Big(\frac{\text{C}-\text{A}}{2}\Big)+\text{c}\sin\frac{\text{C}}{2}\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)=0.$

Find the mean deviation from the median for the following data:

xi	74	89	42	54	91	94	35
fi	20	12	2	4	5	3	4

Find the equations of the circles touching y-axis at $(0, 3)$ and making an intercept of $8$ units on the x-axis.

A circle of radius 4 units touches the coordinate axes in the first quadrant. Find the equations of its images with respect to the line mirrors x = 0 and y = 0.

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): $\frac{\text{px}^2\text{+qx+r}}{\text{ax+b}}$

Let A = {1, 2, 3, ... ,14}. Define a relation R from A to A by R = {(x, y) : 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.

In each of the followin find the equation of the hyperbola satisying the given conditions:

vertices $(0, \pm3)$, foci $(0, \pm5)$ [NCERT]