Question

If U = { x: x <11, x € N}, A = {x : x is divisible by 5}, B = { x : x is divisible by 4}, C = { x : x is divisible by 2}, i) Which two sets are joint? ii) Which two sets are disjoint?​

Answer 1

$\underline{\large\rm{Question}}$

If U = {x: x <11, x € N} such that

• A = {x : x is divisible by 5},
• B = {x : x is divisible by 4},
• C = {x : x is divisible by 2}

$\rule{200pts}{3pts}$

$\succ \underline{ \bf {To \: Find}}$

i) Which two sets are joint?

ii) Which two sets are disjoint?

Solution

The foremost step is to convert the above sets from Set Builder Form to its corresponding Roster Form . Remember that , In set A , B and C no element can be included which is not present in the Universal set since all sets are subsets of the Universal Set .

$\tt{U = ({x: x <11, x \: \epsilon \: N)}} \\ \bf{U = (1,2,3,4,5,6,7,8,9,10)}$

$\tt{A = (x : x \: is \: divisible \: by \: 5}) \\ \bf{A = (5 ,10)}$

$\tt{B = ({x : x \: is \: divisible \: by \: 4})} \\ \bf{B = (4,8)}$

$\tt{C = (x : x \: is \: divisible \: by \: 2)} \\ \bf{C = (2,4,6,8,10)}$

Joint Sets

Those sets which have atleast one element common to them.

Remember that : All sets are subsets of Universal Set so U must make a pair of joint set with every set except U , the pair of Joint Sets are a follow :

1. Set A and C having element 10 common to them .
2. Set B and C having elements 4 & 8 common to them.

Should be noted that Joint sets are also called Overlapping Sets .

Disjoint Sets

Those pair of sets which do not have any element common to them.

• Set A & B is a pair of Disjoint Set.

$\rule{200pts}{3pts}$

$\large\tt{Thankyou}$