Question

Which of the following pairs of sets are disjoint?

• A. {3, 4, 5, 6, 7} and {x: x is a natural number and 7≤ x ≤ 10}
• B. {x: x is a prime number} and {x: x is an even number}
• C. {x: x is an odd number} and {x: x is an even number}
• D. None of these

Answer 1

The correct option is C

{x: x is an odd number} and {x: x is an even number}

Option a : {3, 4, 5, 6, 7}

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

= {7, 8, 9, 10}

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

Option b : {2, 3, 5, 7, 11, - - - -} ∩ {2, 4, 6, 8, 10, - - - -} = {2}

So, given sets are not disjoint sets.

Option c : {1, 3, 5, 7, - - - -} ∩ {2, 4, 6, 8, 10, - - - -} = { }

So, these are disjoint sets.