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 = {`sqrt3, sqrt5, sqrt6`}

P ∪ Q = {3, 4, 5, 6} ∪ {`sqrt3, sqrt5, sqrt6`}

= {3, 4, 5, 6, `sqrt3, sqrt5, sqrt6`}

Q ∪ P = {`sqrt3, sqrt5, sqrt6`} ∪ {3, 4, 5, 6}

= {3, 4, 5, 6, `sqrt3, sqrt5, sqrt6`}

P ∩ Q = { }

Q ∩ P = { }