Question

if universal set ={3,4,5,6,7,8,9,10,11,12,13}
if A ={2x:xEN} and B={3x : xEN}
find the following
1 . n(a)
2 . n(b)
3 . A1 compliment
4 . A union B
5 . A intersection B
pls find all 5 answers correctly step by step want correct answer very fast ​

Answer 1

Given:-

Universal set = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

A = {2x: x belongs to N}

B = {3x: x belongs to N}

Answers:-

1. n(A) = n({6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26}) = 11  ( Same as n(U) )

2. n(B) = n({9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39}) = 11  ( Same as n(U) )

3. A' = U - A = {3, 4, 5, 7, 9, 11, 13}

4. A ∪ B = A + B = {6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 30, 33, 36, 39} = Elements of A and B

5. A ∩ B = {12, 18, 24} =  Elements common in both A and B

Misconception: If A ∪ B = A + B, then A ∩ B = A - B.

Concept: A ∪ B is the union of elements of both sets which results in a set containing elements present in both sets and A ∩ B is the intersection of elements of both sets which results in a set containing elements that are common in both A and B.

All the work is done manually. Nothing is automated.

Note:- The Union and Intersection signs can be obtained by anyone by searching "Sets Symbols" on Google.

ALL THE BEST.