Discrete Math Unit 2

Set Operations

100

This set operation only includes elements in both sets to the left and right of it.

Intersection ∩

200

If A = {1, 4, 5} and B = {1, 2, 6}, what is A ∪ B?

{1, 2, 4, 5, 6}

300

If A = {5, 7, 8} and B = {2, 5, 8, 9}, what is A ∩ B?

{5, 8}

400

If A = {2, 4, 5, 7} and U = integers 1-10 inclusive, what is A'?

A' = {1, 3, 6, 8, 9, 10}

500

When is A - B = B - A?

If A and B are equal

Venn Diagrams

100

Venn diagrams use these to represent sets within a universe.

Circles

200

If a Venn diagram had two sections, one for flying animals and another for insects, name an animal that would be within both circles.

Any flying insect

300

If A = {3, 5, 7}, B = {3, 4, 9} and U = all integers 1-10 inclusive, draw their Venn diagram.

Draw two circles, A and B, overlapping. Their intersection contains 3. The section only in A contains 5 and 7, and the section only in B contains 4 and 9. Draw 1, 2, 6, 8, and 10 outside of the circles but inside of the universe.

400

If A is a subset of B, draw its Venn diagram.

Draw a circle representing B, then a circle inside of it representing A.

500

If A and B are disjoint sets, draw their Venn diagram.

Draw two circles, labelled A and B, that do not overlap.

Cardinality

100

What is the amount of unique elements in a set?

Its cardinality

200

If A is nonempty and B is empty, what is |A| + |B|?

|A|

300

A class has 20 students who like math or science (or both). 12 like math and 16 like science. How many like both?

8

400

If A and B are disjoint, what is |A ∩ B|?

0

500

If A is a subset of B, what is |A ∪ B|?

|B|

Set Theory

100

When is A a subset of B?

All of A's elements are in B

200

When are two sets equal? Use subsets in your answer.

If they are subsets of each other

300

According to DeMorgan's Law, what set is equal to (A∩B)'?

A' ∪ B'

400

What is the intersection of any set and its complement?

The empty set {}

500

If A = {1, 2, 5} and U = integers 1-10 inclusive, what is the union of A and U?

U

Wild Card

100

What shape is an inverter (NOT gate)?

Triangle

200

The logical OR operation resembles which set operation the most?

Union ∪

300

What is the inverse of "If I answer it right, I get 300 points?"

"If I don't answer it right, I don't get 300 points"

400

What is a critical row?

A row in a truth table in which all premises are true.

500

How do you prove that an argument is valid using a truth table?

Look for all critical rows. If each has a true conclusion, the argument is valid.