Discrete Math Exam 1

How to determine how many rows are there in the truth table?

Tautology

Contradiction

Contingency

p -> q = ¬ p V q ?

x^2 = 2 || ∃xeZ (Is there an X in Z), Z = all integers

How do you know if an argument is valid?

p -> q
p
--------
Therefore, q

¬q
p -> q
--------
Therefore, ¬p

p -> q
q -> r
--------
Therefore, p -> r

p v q
¬p
--------
Therefore, q

p
--------
Therefore, p v q

p ∧ q
--------
Therefore, p

p
q
--------
Therefore, p ∧ q

p v q
¬p v r
--------
Therefore, q v r

((p → q) ∧ ¬p) → ¬q

((p → q) ∧ q) → p

What is the precedence of the logical operators in order? In English || Therefore, and, not, biconditional, or

Set N

Set Z

Set Q

Set R

Set C

Closed intervals mean

Open intervals mean

An unordered collection of distinct objects, called elements or members

A set containing one element

A set with no values

Ordered grouping of elements

The number of members in a set

All subsets of a set including the set itself

The set of all ordered pairs (x, y) such that x belongs to A and y belongs to B, such as
A = {1, 2} and B = {3, 4, 5}
answer = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}

Set of all values in sets
A = {1, 2} B = {2, 3}
AUB = {1,2,3}

Set of values common to multiple sets