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} 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) $C ∩ D$

Answer 1

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) $A ∩B$ = {x: x is a even natural number} = B

---

(ii) $A ∩C$ = {x: x is an odd natural number} = C

---

(iii) $A ∩D$ = {x: x is a prime number} = D

---

**(iv) **$B ∩C = \phi$

---

(v) $B ∩D$ = {2}

---

(vi) $C ∩D$ = {x: x is odd prime number}