Question

Test for the commutative property of union and intersection of the sets

P = {x : x is a real number between 2 and 7} and

Q = {x : x is an rational number between 2 and 7}

Answer 1

P = {3, 4, 5, 6}

Q = {${\displaystyle \sqrt{3},\sqrt{5},\sqrt{6}}$}

P ∪ Q = {3, 4, 5, 6} ∪ {${\displaystyle \sqrt{3},\sqrt{5},\sqrt{6}}$}

= {3, 4, 5, 6, ${\displaystyle \sqrt{3},\sqrt{5},\sqrt{6}}$}

Q ∪ P = {${\displaystyle \sqrt{3},\sqrt{5},\sqrt{6}}$} ∪ {3, 4, 5, 6}

= {3, 4, 5, 6, ${\displaystyle \sqrt{3},\sqrt{5},\sqrt{6}}$}

P ∩ Q = { }

Q ∩ P = { }