Tag: different sets

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

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 $n(H' \cap K)$.

  1. $2$
  2. $5$
  3. $7$
  4. $13$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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


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

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

Multiple choice maths introduction to set different sets de morgan's law de morgan's law for set theory
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 :$P'$
  1. $\{-1,-2,-3,-4,-5,-6\}$
  2. $\{1,2,3,4,5,6\}$
  3. $\{0,1,2,3,4,5,6\}$
  4. $\{0,-1,-2,-3,-4,-5,-6\}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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'=${1,2,3,4,5,6}$.

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

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

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
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
Multiple choice maths introduction to set different sets de morgan's law de morgan's law for set theory

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

  1. $\{6,7,9,11,12\}$
  2. $\{5,7,9,11\}$
  3. $\{5,7,9,10,11,12 \}$

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
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
Multiple choice maths introduction to set different sets de morgan's law de morgan's law for set theory

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 }  $ ?  

  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
Reveal answer Fill a bubble to check yourself
D Correct answer
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.