Show that A B = A B implies A = B - Vidyadip

Question

Show that A $\cup$ B = A $\cap$ B implies A = B

✓

Answer

Suppose a $\in$ A.
Then a $\in$ A $\cup$ B. Since A $\cup$ B = A $\cap$ B , a $\in$ A $\cap$ B. So a $\in$ B.
Thus,A ⊂ B. Similarly, if b ∈ B, then b ∈ A ∪ B.
A $\cup$ B = A $\cap$ B, b $\in$ A $\cap$ B. So, b $\in$ A.
Thus, B $\subset$ A. $\Rightarrow$ A = 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 "3 Marks Question" 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 the following limit:
$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{(\text{x}+2)^{\frac{5}{2}}-(\text{a}+2)^{\frac{5}{2}}}{\text{x}-\text{a}}$

Is 68 a them of the A.P. 7, 10, 13, ...?

It is required to seat 5 men and 3 women in a row so that the women occupy the even places. How many such arrangements are possible?

A side of an equilateral triangle is 20cm long. A second equilateral triangle is inscribed in it by joining the mid-points of the sides of the first triangle. This process is continued for third, fourth, fifth, triangles. Find the perimeter of the sixth inscribed equilateral triangle.

Find the equation of the circle which passes through the points (3, 7), (5, 5) and has its centre on the line x - 4y = 1.

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\sin5\text{x}-\sin3\text{x}}{\sin\text{x}}$

Find the equation of the circle passing through the points:
(1, 2), (3, -4) and (5, -6)

Let $\text{T}=\Big\{\text{x}|\frac{\text{x}+5}{\text{x}-7}-5=\frac{4\text{x}-40}{13-\text{x}}\Big\}.$ Is T an empty set? Justify your answer.

If the coefficients of (2r + 1)th and (r + 2)th teram in the expansion of (1 + x)⁴³are equal, find r.

Find the maximum and minimum values of each of the following trigonometrical expressions:
$12\cos\text{x}+ 5\sin\text{x}+4$