Question

If A = {x : x is a natural number}
B = {x : x is an even natural number}C = {x : x is an odd natural number}D = {x : x is a prime number}Find A ∩ B, A ∩ C, A ∩ D, B ∩ C, B ∩ D, C ∩ D.

Answer 1

A = {x : x is a natural number}

A={1,2,3,4,5,6,7,........}

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

B={2,4,6,8,10,12,........}

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

C={1,3,5,7,9,11,13,.......}

D = {x : x is a prime number}

D={2,3,5,7,11,13,17,.....}

A ∩ B =B={2,4,6,8,10,.......}

A ∩ C=C={1,3,5,7,9,11,13,.......},

A ∩ D=D={2,3,5,7,11,13,17,.....},

B ∩ C={0},

B ∩ D={2},

C ∩ D=D-{2}.

Answer 2

Step-by-step explanation:

Given sets are

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, 11, …….}

A ∩ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …….} ∩ {2, 4, 6, 8, 10, ……}

= {2, 4, 6, 8, 10, ……}

A ∩ C = {1, 2, 3,4, 5, 6, 7, 8, 9, 10, …} ∩ {1, 3, 5, 7, 9 }

= {1, 3, 5, 7, 9, ……}

A ∩ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …} ∩ {2, 3, -5, 7, 11,….}

= {2, 3, 5, 7, 11, ……}

B ∩ C = {2, 4, 6, 8, 10, ……} ∩ {1, 3, 5, 7, 9, …….}

= { } = φ

B ∩ D = {2, 4, 6, 8, 10, ……} ∩ {2, 3, 5, 7, 11, ……}

= {2}

C ∩ D = {1, 3, 5, 7, 9, ……} ∩ {2, 3, 5, 7, 11, 13, ……}

= {3, 5, 7, …..}