For any two sets A and B, prove that A-(A-B)=A - Vidyadip

Question

For any two sets A and B, prove that
$\text{A}-(\text{A}-\text{B})=\text{A}\cap\text{B}$

✓

Answer

Let $\text{x}\in \text{A}- \text{(A} - \text{B)}\Leftrightarrow\text{x}\in \text{A}$ and
$\Leftrightarrow\text{x}\in\text{A and x}\in \text{(A} ∩ \text{B)}$
$\Leftrightarrow\text{x}\in\text{A}\cap\text{(A} \cap \text{B})$
$\Leftrightarrow \text{x}\in\text{(A}\cap\text{B})$
$\therefore\text{A} - \text{(A – B) = (A}\cap\text{B})$

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 "5 Marks Questions" from Sets→Sets — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If $\cos\text{x}-\sin\text{x}=\text{a}^3, \sec\text{x}-\cos\text{x}=\text{b}^3,$ than proved that $a^2b^2 (a^2 + b^2) = 1.$

Find the image of the point (2, 1) with respect to the line mirror x + y - 5 = 0.

Given that $\bar{x}$ is the mean and $\sigma^2$ is the variance of n observations $x_1, x_2, \ldots x_n$ Prove that the mean and variance of the observation $ax _1, ax _2, \ldots . ax _{ n }$ are $a \bar{x}$ and $a ^2 \sigma^2$ respectively $(a \neq 0)$

If a, b, c are in A.P., prove that the straight lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent.

Prove that:$\sin^2\text{B}=\sin^2\text{A}+\sin^2\text{(A}-\text{B)}-2\sin\text{A}\cos\text{B}\sin\text{(A}-\text{B)} $

Prove that:
$(\text{A}\cup\text{B})\times\text{C}=(\text{A}\times\text{C})\cup(\text{B}\times\text{C})$

Differentiate the following from the first principle$\text{x}^2\text{e}{^\text{x}}$

Prove that:
$\frac{1}{\sin\text{(x}-\text{b})\sin\text{(x}-\text{b)}}=\frac{\cot\text{(x}-\text{a)}+\tan\text{(x}-\text{b)}}{\cos\text{(a}-\text{b)}}$

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

Find the number of ways in which:

A selection.
An arrangement, of four letters can be made from the letters of the word $\text{'PROPORTION'.}$