Discrete Mathematics Flashcards

Question 1

De Morgan's Law (AND)

Accepted Answer

$
eg (P \land Q) \equiv 
eg P \lor 
eg Q$

Question 2

De Morgan's Law (OR)

Accepted Answer

$
eg (P \lor Q) \equiv 
eg P \land 
eg Q$

Question 3

Commutative Law (AND)

Accepted Answer

$P \land Q \equiv Q \land P$

Question 4

Associative Law (AND)

Accepted Answer

$(P \land Q) \land R \equiv P \land (Q \land R)$

Question 5

Distributive Law (AND over OR)

Accepted Answer

$P \land (Q \lor R) \equiv (P \land Q) \lor (P \land R)$

Question 6

Identity Law (AND)

Accepted Answer

$P \land 	ext{True} \equiv P$

Question 7

Identity Law (OR)

Accepted Answer

$P \lor 	ext{False} \equiv P$

Question 8

Domination Law (AND)

Accepted Answer

$P \land 	ext{False} \equiv 	ext{False}$

Question 9

Domination Law (OR)

Accepted Answer

$P \lor 	ext{True} \equiv 	ext{True}$

Question 10

Idempotent Law

Accepted Answer

$P \land P \equiv P$

Question 11

Double Negation Law

Accepted Answer

$
eg (
eg P) \equiv P$

Question 12

Absorption Law

Accepted Answer

$P \lor (P \land Q) \equiv P$

Question 13

Implication translation $P \implies Q$

Accepted Answer

$
eg P \lor Q$

Question 14

Contrapositive of $P \implies Q$

Accepted Answer

$
eg Q \implies 
eg P$

Question 15

Converse of $P \implies Q$

Accepted Answer

$Q \implies P$

Question 16

Inverse of $P \implies Q$

Accepted Answer

$
eg P \implies 
eg Q$

Question 17

Set Union $A \cup B$

Accepted Answer

$\{x \mid x \in A \lor x \in B\}$

Question 18

Set Intersection $A \cap B$

Accepted Answer

$\{x \mid x \in A \land x \in B\}$

Question 19

Set Difference $A - B$

Accepted Answer

$\{x \mid x \in A \land x 
otin B\}$

Question 20

Set Complement $\overline{A}$

Accepted Answer

$\{x \mid x 
otin A\}$

Question 21

Reflexive Relation

Accepted Answer

$\forall a \in A, (a, a) \in R$

Question 22

Symmetric Relation

Accepted Answer

$\forall a,b \in A, (a, b) \in R \implies (b, a) \in R$

Question 23

Transitive Relation

Accepted Answer

$\forall a,b,c \in A, ((a, b) \in R \land (b, c) \in R) \implies (a, c) \in R$

Question 24

Equivalence Relation

Accepted Answer

A relation that is reflexive, symmetric, and transitive.

Question 25

Partial Order

Accepted Answer

A relation that is reflexive, antisymmetric, and transitive.

Discrete Mathematics

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