Question

Which of the following pair of sets is disjoint?

• A. A = {3, 4, 5, 6, 7} and B = {x : x is a natural number and 7 ≤ x ≤ 10}
• B. P = {x : x is a prime number} and Q = {x : x is an even number}
• C. S = {x : x is an odd number} and T = {x : x is an even number}
• D. None of the above

Answer 1

The correct option is C

S = {x : x is an odd number} and T = {x : x is an even number}

a) A = {3, 4, 5, 6, 7}

B = {x : x is a natural number and 7 ≤ x ≤ 10}

= {7, 8, 9, 10}

A ∩ B = {3, 4, 5, 6, 7} ∩ {7, 8, 9, 10} = {7}. So, A and B are not disjoint sets.

b) P = {2, 3, 5, 7, 11,......} ; Q = {2, 4, 6, 8, 10,........}
P ∩ Q = {2, 3, 5, 7, 11,......} ∩ {2, 4, 6, 8, 10,........} = {2}

So, given sets P and Q are not disjoint sets.

c) S = {1, 3, 5, 7, - - - -} ; T = {2, 4, 6, 8, 10,........}
S ∩ T = {1, 3, 5, 7, - - - -} ∩ {2, 4, 6, 8, 10,........} = { }

$\therefore$ S and T are disjoint sets.