Sets & RelationseasyFree

Sets & Relations: Multiple Multiple Consists Multiples

JEE Maths question with a full step-by-step solution.

Question
If A={x:x is a multiple of 4}A = \{x : x \text{ is a multiple of } 4\} and B={x:x is a multiple of 6}B = \{x : x \text{ is a multiple of } 6\}, then A∩BA \cap B consists of all multiples of:
A1616
B1212correct
C88
D44
Solution
x∈A∩B⇔xx \in A \cap B \Leftrightarrow x is a multiple of both 44 and 6⇔x6 \Leftrightarrow x is a multiple of lcm⁡(4,6)=12\operatorname{lcm}(4, 6) = 12. ∴A∩B={\therefore A \cap B = \{ multiples of 12}.12 \}. Correct answer: (2)
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Sets & Relations · easy
The relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\} on the set A={1,2,3}A = \{1, 2, 3\} is:
Sets & Relations · easy
The relation RR is defined in A={1,2,3}A = \{1, 2, 3\} by aRbaRb if ∣a2−b2∣≤5|a^2 - b^2| \le 5. Which of the following is false?
Sets & Relations · easy
If AA is the set of even natural numbers less than 88 and BB is the set of prime numbers less than 77, then the number of relations from AA to BB is:
Sets & Relations · easy
The relation RR is defined on the set of natural numbers as {(a,b):a=2b}\{(a, b) : a = 2b\}. Then R−1R^{-1} is given by:

Solve more, learn faster

Sign up free to solve more JEE Maths questions and explore doMath — timed drills, mastery sprints, bookmarks, and chapter-wise progress tracking.

Sign up freeExplore doMath