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 AnB, AnC, AnD, BnC, BnD, CnD.
Answers
A={1,2,3,4,5,6,7,8,9,10....}
B={2,4,6,8,10}
C={1,3,5,7,9}
D={2,3,5,7,}
AnB ={2,4,6,10}
AnC={1,3,5,7,9}
AnD={3,5,7}
BnC={ 0 }
BnD={2}
CnD={3,5,7}
Answer:
A ∩ B = {2, 4, 6, 8, 10, 12, . . . . . . . .}
A ∩ C = {1, 3, 5, 7, 9, 11, 13, . . . . . . . }
A ∩ D = {2, 3, 5, 7, 11, 13, . . . . . . . . .}
B ∩ C = ∅
B ∩ D = {2}
C ∩ D = {3, 5, 7, 11, 13}
Step-by-step explanation:
According to the question,
A = {1, 2, 3, 4, 5, 6, 7, . . . . . . . .}
B = {2, 4, 6, 8, 10, 12, . . . . . . . .}
C = {1, 3, 5, 7, 9, 11, 13, . . . . . . . }
D = {2, 3, 5, 7, 11, 13, . . . . . . . . .}
Therefore,
(i) A ∩ B
A ∩ B = {2, 4, 6, 8, 10, 12, . . . . . . . .}
As every even natural number is a natural number, therefore, A ∩ B = B
(ii) A ∩ C
A ∩ C = {1, 3, 5, 7, 9, 11, 13, . . . . . . . }
As every odd natural number is a natural number, therefore, A ∩ C = C
(iii) A ∩ D
A ∩ D = {2, 3, 5, 7, 11, 13, . . . . . . . . .} = D
As every prime number is a natural number, therefore, A ∩ D = D
(iv) B ∩ C
B ∩ C = ∅
As there is no natural number which is odd as well as even, therefore,
B ∩ C = ∅
(v) B ∩ D
B ∩ D = {2}
As the only prime number which is even is 2, therefore, B ∩ D = {2}
(vi) C ∩ D
C ∩ D = {3, 5, 7, 11, 13} = D - {2}
Every odd prime number lies in this set.
As D is the set of prime numbers, therefore, C ∩ D will be the set D excluding the element 2.
=> C ∩ D = D - {2}