Tag: introduction to set

Quizzes (6) Questions (82)

Questions Related to introduction to set

Multiple choice mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

If $A={\theta :\tan \theta -\tan^2\theta > 0}, B={\theta :|\sin \theta | < 1/2}$ find $A\cap B$.

  1. $\left(0 , \cfrac{7\pi}{6}\right)$
  2. $\left(0 , \cfrac{\pi}{6}\right)$
  3. $\left(0 , -\cfrac{\pi}{6}\right)$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\tan \theta - \tan ^2 \theta > 0$ is only true when 

$0<\tan \theta < 1$
or,$ 0< \theta < \cfrac{\pi}{4}$
$A = (0,\cfrac{\pi}{4})$
$|\sin \theta| < \cfrac{1}{2}$
$-\cfrac{1}{2} < \sin \theta < \cfrac{1}{2}$
$B = (-\cfrac{\pi}{6} , \cfrac{\pi}{6})$
$A \cap B = (0 , \cfrac{\pi}{6})$

Multiple choice maths introduction to set intervals subsets subsets and supersets

The number of subsets of the set $A={ { a } _{ 1 },{ a } _{ 2 },.........{ a } _{ n }} $ which contain even number of elements is

  1. ${ 2 }^{ n-1 }$
  2. ${ 2 }^{ n }-1$
  3. ${ 2 }^{ n }-2$
  4. ${ 2 }^{ n }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
The total no of subsets of $A$ is the cardinality of the power set of $A$. 

So, if $|A|=n$ then $|P(A)|=2^n$. 

Therefore total no of subsets of $A$ is $2^n$.

Similarly,

The even number of events is given by, $2^{n-1}$