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

Question

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

✓

Answer

True.
$\text{L.H.S.}=(\text{A}-\text{B})\cup(\text{A}\cap\text{B})$
$=\big[(\text{A}-\text{B})\cup\text{A}\big]\cap[(\text{A}-\text{B})\cup\text{B}\big]$
$=\text{A}\cap(\text{A}-\text{B})=\text{A}=\text{R.H.S.}$
$\text{L.H.S.}=\text{R.H.S.}$
Hence, given statement is true.

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

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

$2\sec\text{x}+3\cot\text{x}-4\tan\text{x}$

Prove that:
$\sin\frac{13\pi}{3}\sin\frac{8\pi}{3}+\cos\frac{2\pi}{3}\sin\frac{5\pi}{6}=\frac{1}{2}$

Find the value of the following trigonomentric ratio:
$\text{cosec}\Big(-\frac{20\pi}{3}\Big)$

Differentiate the following functions.
$(3\text{x}+5)(1+\tan\text{x})$

Find the equation of a line that cuts off equal intercepts on the coordinate axis and passes through the point (2, 3).

Find the conjugate of $\frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)}$

Find the A.M. between:
(x - y) and (x + y)

Show the following quadratic equation:
x² - x + (1 + i) = 0

Solve the following system of equations in R.
$3\text{x}-1\geq5, \ \text{x}+2>-1$

Find the distance between the parallel lines 3x – 4y + 7 = 0 and 3x – 4y + 5 = 0