Tag: intervals

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Questions Related to intervals

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, $2^{n-1}$
Multiple choice maths set concepts intervals subsets subsets and supersets

Let $A = {a, b, c}, B = {a}, C = {a, b}$ then,  which set is the superset of $C$? 

  1. Set $A$
  2. Set $B$
  3. Set $A$ and Set $B$

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

$\text{Clearly, set A contain all elements of set C}$
$\Rightarrow \text{A is superset of C}$

Multiple choice maths set concepts intervals subsets subsets and supersets

If U = {1, 2, 3, .......}; A = {2, 4, 6, 8, .......}; B = {1, 3, 5, .......}, then find (A $\cup$ B)'.

  1. A'

  2. B

  3. A
  4. $\phi$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given,
$U=(1, 2, 3,....)$
$A=\{2, 4, 6, 8,...\}$
$B=\{1, 3, 5, 7,....\}$

We know,
$(A\cup B)'=U-(A\cup B)$

here
$A\cup B=\{1, 2, 3,....\}=U$

so $(A\cup B)'=\phi$.
Multiple choice maths set concepts intervals subsets subsets and supersets

The number of subsets with two elements, of the set $S+{1,2,3,4,.....,10}$ such that minimum of the two numbers is less than $6$ is 

  1. $35$
  2. $38$
  3. $30$
  4. $40$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We need subsets {a, b} from {1, ..., 10} where min(a, b) < 6. If min is 1, there are 9 choices for the other number. If min is 2, there are 8 choices. If min is 3, there are 7. If min is 4, there are 6. If min is 5, there are 5. Sum = 9+8+7+6+5 = 35.

Multiple choice maths set concepts intervals subsets subsets and supersets

Which of the following sets is a universal set for the other four sets? 

(a) The set of even natural numbers 

(b) The set of odd natural numbers

(c) The set of natural numbers 

(d) The set of negative numbers 

(e) The set of integers 

  1. $(e)$
  2. $(a)$
  3. $(b)$
  4. $(c)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that $\mathbb{N} \subset \mathbb{Z}$ where $\mathbb{N}$ represents set of natural numbers and $\mathbb{Z}$ represents set of all positive and negative integers.

Since $\mathbb{N} \subset \mathbb{Z}$,

                                 $(a),(b),(c)$ are subsets of $(e)$        $...(1)$

Since $\mathbb{Z}$ represents set of all positive and negative integers.

                                      $(d)$ is a subset of $(e)$                   $...(2)$

From $(1)$ and $(2)$ we get

$(a),(b),(c),(d)$ are subsets of $(e)$.

Hence $(e)$ is the universal set for the other four sets.

Multiple choice maths set concepts intervals subsets subsets and supersets

State whether the following statement is true or false
 $0$ $\epsilon$ $\phi$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We have to state whether the statement "$0 \in \phi$" is true or false.

We know that, $\phi$ represents null set.

The null set, also called the empty set, is the set that does not contain any element.

Thus by the definition of null set, $0 \notin \phi$

Hence the given statement is false.