COMEDK2024MathematicsSets and RelationsActual
If a N = a x: x N , then 3 N 7 N is
Options
- A10 N
- B4 N
- C21 N
- D3 N
Correct answer
C. 21 N
Step-by-step solution
The set a N is defined as the set of all multiples of a where a N and N = 1, 2, 3, . The set 3 N consists of all natural numbers that are multiples of 3 , i.e., 3 N = 3, 6, 9, 12, 15, 18, 21, 24, . The set 7 N consists of all natural numbers that are multiples of 7 , i.e., 7 N = 7, 14, 21, 28, 35, . The intersection 3 N 7 N consists of all natural numbers that are multiples of both 3 and 7 . A number is a multiple of both 3 and 7 if and only if it is a multiple of the least common multiple of 3 and 7 . Since 3 and