Question

State which of the following are joint sets? Which are disjoint sets? Give reason. A1 ={2,3,5,7,11,13}; A2 = {set of primes below 20} B1 {All indians}, B2 {All andhras}​

Answer 1

Step-by-step explanation:

Given ;-

A1 ={2,3,5,7,11,13}; A2 = {set of primes below 20}

B1 = {All indians}, B2 = {All andhras}

To find :-

State which of the following are joint sets? Which are disjoint sets? Give reason.

Solution :-

I)

Given sets are

A1 ={2,3,5,7,11,13} and

A2 = {set of primes below 20}

=> A2 = { 2,3,5,7,11,13,17,19}

A1 ∩ A2 = { 2,3,5,7,11,13} n { 2,3,5,7,11,13,17,19}

=> A1 ∩ A2 = { 2,3,5,7,11,13 }

So , A1 and A2 having common elements.

A1 and A2 are not disjoint sets .

They are joint sets.

II)

Given sets are

B1 = {All indians}

=>B1 = { All Andhras, All Tamiliand All Kannadians, ...}

B2 = {All Andhras}

B1 ∩ B 2 = {All indians} ∩ {All andhras}

=> B1 ∩ B2 = { All Andhras, All Tamiliand All Kannadians, ...} ∩ {All Andhrasndhras}

Since India contains all states

B1 ∩ B2 = { All Andhras }

So , A1 and A2 having common elements.

A1 and A2 are not disjoint sets .

They are joint sets.

Answer :-

I) A1 and A2 are joint sets .

II) B1 and B2 are joint sets.

Used formulae:-

»»If A and B sets having no common element they are called disjoint sets.

»»If A ∩ B = { } then A and B are disjoint sets