Unions, Complements, and Intersections

Union, Intersection and Compliment

by Ginger Remy

​Union

​All the of the elements in both A and B.

​

​

If A={1,2,3} and B={2,3,4,5,6},

then AUB ={1,2,3,4,5,6}

​Intersection

​Elements that are common to both sets

​

If P={friday, saturday, sunday} & Q= {sunday, monday}

​

Then P n Q= {sunday}

Disjoint Sets

​When two sets have no elements in common.

​If A={2,4,6,8} and B={3,9,10,12}

​

Then A n B= { }

​Complement

​Everything that is not in the given set.

​

​If U= {p,q,r,s,t,u,v,w}

​and V={q,t,w}

​

​then V'={p,r,s,u,v}

Open Ended

What does this symbol represent?

Open Ended

What does this symbol represent?

Open Ended

Write the symbol for S complement.

Multiple Choice

If A = {5, 6, 7} and B = {6, 8, 10, 12}; then A ∪ B = {5, 6, 7, 8, 10, 12}.

• True

• False

• t

Multiple Choice

If P = {a, b, c} and Q = {b, c, d}; then p intersection Q = {b, c}.

• True

• False

Multiple Choice

Union of two sets is the set of elements which are common to both the sets.

• True

• False

Multiple Choice

Two disjoint sets have atleast one element in common.

• True

• False

Multiple Choice

If two given sets have no elements common to both the sets, the sets are said to me disjoint.

• True

• False

Multiple Choice

If A and B are two disjoint sets then A ∩ B = { }, the empty set.

• True

• False

Open Ended

If Set A = {2, 4, 6, 8, 10, 12}, set B = {3, 6, 9, 12, 15} and set C = {1, 4, 7, 10, 13, 16}. Find;

(i) A ∪ B

(ii) A ∩ B

(iii) B ∩ A

(iv) B ∪ A

(v) B ∪ C

(vi) Is A ∪ B = B ∪ A?

(vii) Is B ∩ C = B ∪ C?

Open Ended

If A = {1, 3, 7, 9, 10}, B = {2, 5, 7, 8, 9, 10}, C = {0, 1, 3, 10}, D = {2, 4, 6, 8, 10}, E = {negative natural numbers} and F = {0}

Find:

(i) A ∪ B

(ii) E ∪ D

(iii) C ∪ F

(iv) C ∪ D

(v) B ∪ F

(vi) A ∩ B

(vii) C ∩ D

(viii) E ∩ D

(ix) C ∩ F

(x) B ∩ F

(xi) (A ∪ B) ∪ (A ∩ B)

(xii) (A ∪ B) ∩ (A ∩ B)

Open Ended

If A={a,b,c,d,e,f,g} and B={a,n,f,j,g,h}. List the members of

i. B'

ii. A'