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 "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 $\text{f(x)}=\log_\text{e}(1-\text{x})$ and $\text{g(x)}=[\text{x}],$ then determine the following functions:
$\frac{\text{f}}{8}$

Find the value of the expression
$3[\sin^4\Big(\frac{3\pi}{2}-\alpha\Big)+\sin^4(3\pi+\alpha)]-2[\sin^6\Big(\frac{\pi}{2}+\alpha\Big)+\sin^6(5\pi-\alpha)]$

Prove that: $\frac{\sin\text{(A-B)}}{\cos\text{A}\cos\text{B}}+\frac{\sin\text{(B-C)}}{\cos\text{B}\cos\text{C}}+\frac{\sin\text{(C-A)}}{\cos\text{C}\cos\text{A}}=0$

Prove that:
$\cos\text{A}+\cos3\text{A}+\cos5\text{A}+\cos7\text{A}=4\cos\text{A}\cos2\text{A}\cos4\text{A}$

A sequence $x_1, x_2, x_3, ...$ is defined by letting $x_1 = 2$ and $\text{x}_{\text{k}}=\frac{\text{x}_{\text{k}}-1}{\text{n}}$ for all natural numbers k, $\text{k}\geq2.$ Show that $\text{x}_{\text{n}}=\frac{2}{\text{n}!}$ for all $\text{n}\in\text{N}.$

Prove the following by the principle of mathematical induction:
$\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{(\text{4n-1)(4n+3)}}=\frac{\text{n}}{3(\text{4n}+3)}$

For what value of λ are the three lines 2x - 5y + 3 = 0, 5x - 9y + λ = 0 and x − 2y + 1 = 0 concurrent?

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions?

Using distance formula prove that the following points are collinear:
A(4, -3, -1), B(5, -7, 6) and C(3, 1, -8)

Find the equation of na ellipse whose foci are at $(\pm3,\ 0)$ and which passes through (4, 1).