KnowledgeBoat Logo
|

Mathematics

Let P = {x : x is a factor of 18} and Q = {x : x is a factor of 24}.

(i) Write each one of P and Q in Roster form.

(ii) Find:

(a) P ∪ Q

(b) P ∩ Q

Sets

1 Like

Answer

(i) Write each one of P and Q in Roster form.

P = {x : x is a factor of 18}

Factors of 18 are numbers that divide 18 exactly: 1, 2, 3, 6, 9, 18.

P = {1, 2, 3, 6, 9, 18}

And

Q = {x : x is a factor of 24}

Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.

Q = {1, 2, 3, 4, 6, 8, 12, 24}

∴ P = {1, 2, 3, 6, 9, 18}, Q = {1, 2, 3, 4, 6, 8, 12, 24}

(ii) Find:

(a) P ∪ Q

P = {1, 2, 3, 6, 9, 18}

Q = {1, 2, 3, 4, 6, 8, 12, 24}

P ∪ Q = {1, 2, 3, 6, 9, 18} ∪ {1, 2, 3, 4, 6, 8, 12, 24}

∴ P ∪ Q = {1, 2, 3, 4, 6, 8, 9, 12, 18, 24}

(b) P ∩ Q

P = {1, 2, 3, 6, 9, 18}

Q = {1, 2, 3, 4, 6, 8, 12, 24}

P ∩ Q = {1, 2, 3, 6, 9, 18} ∩ {1, 2, 3, 4, 6, 8, 12, 24}

∴ P ∩ Q = {1, 2, 3, 6}

Answered By

1 Like

Related Questions