Question

State which pairs of sets are disjoint or overlapping?
(i) A={f, i, a, s} and B={a, n, f, h, s}
(ii) C ={x : x is a prime number, x >2} and D ={x:x is an even prime number}
(iii) E={x : x is a factor of 24} and F={x : x is a multiple of 3, x < 30}

Answer 1

Given :  (i) A={f, i, a, s} and B={a, n, f, h, s}

(ii) C ={x : x is a prime number, x >2} and D ={x:x is an even prime number}

(iii) E={x : x is a factor of 24} and F={x : x is a multiple of 3, x < 30

To Find : sets are disjoint or overlapping  

Solution:

Over lapping sets  - have atleast one common elements

Disjoint sets does not have any common element

A={f, i, a, s} and B={a, n, f, h, s}

A ∩ B = { f , s }

overlapping  set

C ={x : x is a prime number, x >2} and D ={x:x is an even prime number}

C = { 3 , 5 , 7 , 11 ...............}

D = { 2 }

C ∩ D = { }  = Ф

Disjoint sets.

E={x:x is afactor of 24}

E= { 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24 }

F={x:x is a multiple of 3, x<30}

F = {3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 }

E ∩ F  = { 3 , 6 , 12 , 24 }

Over lapping sets

Learn more:

https://brainly.in/question/10495660

andB ( x:x is a dolution of x^2+6x+8=o )

https://brainly.in/question/17285000

B= {x:xe N, and 'x' is multiple of 8}C

https://brainly.in/question/14732925

Answer 2

(i) A={1,2,3,4}

B={x:x is a natural number and 4≤x≤6}={4,5,6}

Now, A∩B={1,2,3,4}∩{4,5,6}={4}

Therefore, this pair of sets are not disjoint.

(ii) A={a,e,i,o,u}

B={c,d,e,f}

A∩B={e}

Therefore, this pair of sets are not disjoint.

(iii) A={x:x is an even integer}

B={x:xis an odd integer}

A∩B=ϕ

Therefore, this pair of sets is disjoint.