KCET2024MathematicsSets and Relations
Two finite sets have m and n elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n , respectively are
Options
- A7,6
- B5,1
- C6,3
- D8,7
Correct answer
C. 6,3
Step-by-step solution
Let set A have m elements and set B have n elements Now, 2^m-2^n=56 2^n (2^ m-n -1 )=8 7 2^n (2^ m-n -1 )=2^3 7 On comparing both sides, we get 2^n=2^3 or 2^ m-n -1=7 Now, n=3 ....(i) So, 2^ m-n -1=7 2^ m-n =8 m-n=3 ....(ii) From Eqs. (i) and (ii), we get m=6 and n=3