Question

If A and B be two sets containing $4$ and $8$ elements respectively, what can be the maximum number of elements in $A\cup B$? Find also, the minimum number of elements in $(A\cup B)$?

• A. Maximum number of elements $=12$
  Minimum number of elements $=8$
• B. Maximum number of elements $=14$
  Minimum number of elements $=8$
• C. Maximum number of elements $=12$
  Minimum number of elements $=9$
• D. Maximum number of elements $=14$
  Minimum number of elements $=7$

Answer 1

The correct option is A Maximum number of elements $=12$

Minimum number of elements $=8$

R.E.F image

$i)\therefore (A\cup B)=12$

max. element if ${}^{\prime }{A}^{\prime }$ & ${}^{\prime }{B}^{\prime }$

distant

R.E.F image

$ii)\Rightarrow (A\cup B)=8$

min. if of ${}^{\prime }{B}^{\prime }$ inside of A.