Let A and B be two stes such that: n(P)= 20,n(A )=42 and n(A )=4.… - Vidyadip

Question

Let A and B be two stes such that: $\text{n(P)}= 20,$$\text{n(A}\cup\text{B)=42 and n(A}\cap\text{B})=4.$ Find:
$\text{n(B} - \text{A)}.$

✓

Answer

To find: $\text{B}- \text{A}$
On a similar lines we have B is the disjoint union of $\text{B} - \text{A}$ and $\text{A}\cap\text{B}$
i.e., $\text{B = (B} - \text{A)}\cup\text{(A}\cap\text{B})$
$\therefore\text{ n(B)=n(B}- \text{A)}+\text{n}\text{(A}\cap\text{B})$
$\Rightarrow26 = \text{n(B} - \text{A)} + 4$
$\Rightarrow\text{n(B} - \text{A)} = 26 - 4$
$= 22$
$\therefore\text{n(B} - \text{A)} = 22.$

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

Prove the following by the principle of mathematical induction:
$1^2 + 2^2 + 3^2 +...+ \text{n}^2=\frac{\text{n}(\text{n}+1)(2\text{n}+1)}{6}$

Determine the number of 5 card combination out of a deck of if there is one ace in each combination.

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\frac{\pi}{2}}}\frac{\big(\frac\pi2-\text{x}\big)\sin\text{x}-2\cos\text{x}}{\big(\frac\pi2-\text{x}\big)+\cot\text{x}}$

Prove the following by the principle of mathematical induction:
$5^{2n+2} + 24n - 25$ is divisible by $576$ for all $\text{n}\in\text{N}$

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

The owner of a milk store finds that he can sell 980 litres milk each week at Rs 14 per liter and 1220 liters of milk each week at Rs 16 per liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs 17 per liter.

The vertices of a quadrilateral are A (-2, 6), B (1, 2), C (10, 4) and D (7, 8). Find the equation of its diagonals.

Reduce each of the following expressions to the sine and cosin of a single expression:
$24\cos\text{x}+7\sin\text{x}$

Prove the following by the principle of mathematical induction:
$1 + 3 + 3^2 + ... + 3^{\text{n}-1}=\frac{3^\text{n}-1}{2}$

$\text{If}\ \sin2\text{A}=\lambda\sin2\text{B},$ prove that:
$\frac{\tan(\text{A+B})}{\tan(\text{A}-\text{B})}=\frac{\lambda+1}{\lambda-1}$