If $A = {x : x$ is a natural number $}, B = {x : x$ is an even natural number $} C = {x : x$ is an odd natural number $}$ and $D = {x : x$ is a prime number $},$ find
(i) $A \cap B$
(ii) $A \cap C$
(iii) $A \cap D$
(iv) $B \cap C$
(v) $B \cap D$
(vi) $C \cap D$

Open in App

Solution

$A = {x : x is a natural number} = {1, 2, 3, 4, 5.....}$
$B = {x : x is an even natural number} = {2, 4, 6, 8 . . . . .}$
$C = {x : x is an odd natural number} = {1, 3, 5, 7, 9 . . . . . . .}$
$D = {x : x is a prime number} = {2, 3, 5, 7 . . . .}$
(i) $A \cap B = {x : x is a even natural number} = B$
(ii) $A \cap C = {x : x is an odd natural number} = C$
(iii) $A \cap D = {x : x is a prime number} = D$
(iv) $B \cap C = ϕ$
(v) $B \cap D = {2}$
(vi) $C \cap D = {x : x is odd prime number}$

Suggest Corrections

Similar questions

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

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

(i) A ∩ B

(ii) A ∩ C

(iii) A ∩ D

(iv) B ∩ C

(v) B ∩ D

(vi) C ∩ D

A = {x : x i s a n a t u r a l n u m b e r}, B = {x : x i s e v e n n a t u r a l n u m b e r},

C - {x : x i s a n o d d n a t u r a l n u m b e r}

D = {x : x i s a' n u m b e r}

C \cap D

If A = {x: x is a natural number}

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

C = {x: x is a prime number}

Then (A $\cup$ B) $\cap$ C =

If A = {x: x is a prime number}

B = {x: x is an odd natural number}

Then A ∩ B is

Join BYJU'S Learning Program