For any two sets A and B, show that the following statements are … - Vidyadip

Question

For any two sets A and B, show that the following statements are equevalent: $\text{A}-\text{B}=\phi.$

✓

Answer

We new show that (2) ⇒ (3) So assume that $\text{A - B}=\phi$ To show: $\text{A}\cup\text{B}=\text{B}$ $\because$ Every element of A is an element of B $[\because\text{A}-\text{B}=\phi$ only when ther is some element in A which is not in B$]$ So $\text{A}\subset\text{B}$ and therefore $\text{A}\cup\text{B}=\text{B}$ So (2) ⇒ (3) 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 "(Each question 3 marks)" from Sets→Sets — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Classify the following pairs of lines as coincident, parallel or intersecting: 3x + 2y - 4 = 0 and 6x + 4y - 8 = 0.

Given A = {1, 2, 3}, B = {3, 4}, C ={4, 5, 6}, find $(\text{A}\times\text{B})\cap(\text{B}\times\text{C})$

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}-3}-\frac{2}{\text{x}^2-4\text{x}+3}\Big)$

Find the distance between $P(x_1, y_1)$ and $Q(x_2, y_2)$ when PQ is parallel to the y-axis

Differentiate the following function with respect to x:$(\text{ax}+\text{b})^\text{n}(\text{cx}+\text{d})^\text{m}$

Find the mean deviation about the mean for the following data.

$x_i$	2	5	6	8	10	12
$f_i$	2	8	10	7	8	5

Point R(h, k) divides a line segment between the axis in the ratio 1 : 2. Find equation of the line.

How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?

Show that the statement “For any real numbers a and b, $\text{a}^2=\text{b}^2$ implies that $\text{a = b}$” is not true by giving a counter-example.

Find the modulus and argument of the following complex numbers and hence express each of them in the polar form: $\sin120^\circ-\text{i}\cos120^\circ$