Tag: de morgan's law for set theory

Questions Related to de morgan's law for set theory

$(A\cup B)' $  $=$

mathematics and statistics set language de morgan's law for set theory complement of sets different sets de morgan's law

  1. $A' \cup B'$

  2. $A' \cap B'$

  3. $A$

  4. 0

Show answer
Correct Option: B

Let the universal set, $\xi$ = {$x : 1 \leq  x \leq  15$ and x is an  integer} set H = {x : x is a multiple of 3} and set K = {x : x is an even number}. Find $n(H' \cap K)$.

mathematics and statistics sets and relations de morgan's law for set theory complement of sets different sets de morgan's law

  1. $2$

  2. $5$

  3. $7$

  4. $13$

Show answer
Correct Option: B
Explanation:

H' includes all numbers from 1 to 15 that are not multiples of 3.


$H'\cap K ={2,4,8,10,14}$

$n(H'\cap K) =5$

State True or False
$\displaystyle A\cup A'=\phi $

maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

False because $\displaystyle A\cup A'=\cup  $

Given, universal set = {$x \,\,\epsilon\,\, Z$ : $- 6 < x \leq 6$}, N = {$n$ : $n$ is a non-negative number} and P = {$x$ : $x$ is a nonpositive number}. Find :$P'$
maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. ${-1,-2,-3,-4,-5,-6}$ 

  2.  ${1,2,3,4,5,6}$ 

  3. ${0,1,2,3,4,5,6}$ 

  4. ${0,-1,-2,-3,-4,-5,-6}$ 

Show answer
Correct Option: B
Explanation:

Universal set includes ${-5,-4,-3,-2,-1,0,1,2,3,4,5,6}$


P=${-5.-4.-3,-2,-1,0}$.

Hence P' only has the elements in option B. It does not contain 0.
P'=${1,2,3,4,5,6}$.

If the universal set ${x\in W ,3<x≤12} ,A={5,7,9}$, then $A'=$

maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. ${3,6,8,10,11,12}$

  2. ${4,6,8,10,11,12}$

  3. ${6,8,10,11,12}$

  4. None of the above

Show answer
Correct Option: B
Explanation:
Given universal set is $\{x\in W ,3<x≤12\}$
It can be written as a set $\{4,5,6,7,8,9,10,11,12\}$
$A$ is given as $A=\left\{5,7,9\right\}$
$\therefore A'=W-A=$ All the elements in the universal set but not in set $A$
         $ =\{4,6,8,10,11,12\}$
Hence, option B is correct

Let  $U={x: \in, W: 3<x< 12} $, $B={4,6,8,10}$ . $B'$

maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. ${6,7,9,11,12}$

  2. ${5,7,9,11}$

  3. ${5,7,9,10,11,12 }$

  4. None of the above

Show answer
Correct Option: B
Explanation:
Given universal set is $\{x\in W ,3<x<12\}$
It can be written as a set $\{4,5,6,7,8,9,10,11\}$
$B$ is given as $B=\left\{4,6,8,10\right\}$
$\therefore B'=W-B=$ All the elements in the universal set but not in set $B$
         $ =\{5,7,9,11\}$
Hence, option B is correct

Let $S={1,2,3,4,5,6,7}$ and let $A={2,5,7}$ then $A'$ is

maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. ${1,3,6}$

  2. ${1,3,4,6}$

  3. ${1,4,6}$

  4. none of these

Show answer
Correct Option: B
Explanation:

Given, $S={1,2,3,4,5,6,7}$ and let $A={2,5,7}$.

Now, $A'=S-A={1,3,4,6}$.

If AandB are subsects of the universal set X and n(X)=$50,$n(A)=$35$,n(B)=20 Find

maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. $n(A\bigcup {B)} $

  2. $n(A\bigcap {B)} $

  3. $n(A`\bigcap {B)} $

  4. $n(A\bigcap {B`} )$

Show answer
Correct Option: A

For any two sets A and B, A' - B' is equal to

maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. A -B

  2. B - A

  3. A - A'

  4. A - B'

Show answer
Correct Option: B
Explanation:

$A' -B' = B-A$

since $ -X' =X \ and\ X'=-X$

If the universal set is U = $ \displaystyle \left { 1^{2},2^{2},3^{2},4^{2},5^{2},6^{2} \right }  $   What is the complement of the intersection of set A = $ \displaystyle \left { 2^{2},4^{2},6^{2} \right }  $ and set B=$ \displaystyle \left { 2^{2},3^{2},4^{2} \right }  $ ?  

maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. $ \displaystyle \left { 2^{2},4^{2} \right } $

  2. $ \displaystyle \left { 1^{2},5^{2} \right } $

  3. $ \displaystyle \left { 1^{2},5^{2},6 ^{2} \right } $

  4. $ \displaystyle \left { 1^{2},3^{2},5^{2},6^{2} \right } $

  5. Answer required

Show answer
Correct Option: D
Explanation:

$A\cap B={2^2,4^2}$
$\bar{A\cap B}=U-(A\cap B)={1^2,3^2,5^2,6^2}$
Option D is correct.