Question

A = { x : x is a natural number } B = {x : x an even natural number}

C = {x : x an odd natural number } D = {x : x is a prime} then find

i) A - B ii) B ∩ D iii) A – C iv) B ∪ C​

Answer 1

Step-by-step explanation:

Given :-

A = { x : x is a natural number }

B = {x : x an even natural number}

C = {x : x an odd natural number }

D = {x : x is a prime}

To find :-

Find the following

i) A - B

ii) B ∩ D

iii) A – C

iv) B ∪ C

Solution :-

Given that :-

A = { x : x is a natural number }

A = { 1,2,3,4,...} ----------(1)

B = {x : x an even natural number}

B = { 2,4,6,8,...} ----------(2)

C = {x : x an odd natural number }

C = { 1,3,5,7,...} -----------.(3)

D = {x : x is a prime}

D = { 2,3,5,7...} -----------(4)

Now,

i) A - B :-

A- B

= { 1,2,3,4,...} - { 2,4,6,8,...}

A- B = { 1,3,5,7...}

ii)B ∩ D :-

B ∩ D = { 2,4,6,8,...} ∩ { 2,3,5,7...}

B ∩ D = { 2}

iii) A – C :

A – C = { 1,2,3,4,...} - { 1,3,5,7,...}

A – C = { 2,4,6,8,... }

iv)B ∪ C:-

B ∪ C = { 2,4,6,8,...} ∪ { 1,3,5,7,...}

B ∪ C = {1,2,3,4,5,6,7,8,...}

Answer:-

i)A- B = { 1,3,5,7...} = C

ii)B ∩ D = { 2}

iii)A – C = { 2,4,6,8,... } = B

iv)B ∪ C = {1,2,3,4,5,6,7,8,...} = A

Used formulae:-

If A and B are two sets then

• A ∪ B is the set of elements in either A or in B or in both.

• A ∩ B is the set of common elements in both A and B.

• A – B is the set of elements in only A i.e.The elements belongs to A and doen not belongs to B.

• B – Ais the set of elements in only B i.e.The elements belongs to B and doen not belongs to A.