For all sets A, and B, (A )-B=A - B. - Vidyadip

Question

For all sets A, and B, $(\text{A}\cup\text{B})-\text{B}=\text{A} - \text{B}.$

✓

Answer

$\text{L.H.S.}=(\text{A}\cup\text{B})-\text{B}$
$=(\text{A}\cap\text{B})\cap\text{B}'\ \big[\because \text{A}-\text{B}=\text{A}\cap\text{B}'\big]$
$=(\text{A}\cap\text{B}')\cup(\text{B}\cap\text{B}')$
$=(\text{A}\cap\text{B}')\cup\phi$
$=\text{A}\cap\text{B}'=\text{A}-\text{B}=\text{R.H.S.}$
$\text{L.H.S.}=\text{R.H.S.}$
Hence 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 "2 Marks Questions" from Sets→Sets — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate $\mathop {\lim }\limits_{x \to - 1} \frac{{{x^{10}} + {x^5} + 1}}{{x - 1}}$

Find the derivative of function $\frac{{1 + \frac{1}{x}}}{{1 - \frac{1}{x}}}$ (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).

Evaluate $\mathop {\lim }\limits_{x \to 0} \frac{{ax + b}}{{cx + 1}}$

A committee of 6 members is to be formed out of 8 men and 5 women. In how many ways can this committee be formed while in each committee :
(i) there should be only 2 men,
(ii) there should be only 2 women,
(iii) there should be at least two women,
(iv) there should be at least two men.

Find the equation of a line for which:
$\text{p}=8,\alpha=300^\circ$

Find the value of the following trigonomentric ratio:
$\cos\Big(\frac{19\pi}{6}\Big)$

Write down all possible subsets of A = (1, {2, 3}).

Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball.

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{x+2}-\text{e}^2}{\text{x}}$

Differentiate the following function with respect to $\text{x}:$

$(\text{x}^3+\text{x}^2+1)\sin\text{x}$