CP 5 Intro to Formal Logic

Question 1

Given 2 statements P and Q the _____is P∧Q and the ____ is PVQ

Answer 1

conjunction
disjucntion

Question 2

what is a conjunction

Answer 2

P∧Q (P and Q)
“both akira and paul have cats”

Question 3

what is a disjunction

Answer 3

PVQ (P or Q)
“Either Sam or Max has a dog”

Question 4

TF, PVQ is false when only P and Q are false, P∧Q is true only when P and Q are true

Answer 4

T, Look at the mother truth table

Question 5

What is a conditional statement/implication

Answer 5

Given statements P and Q, P then Q (P⇒Q)
“P implies Q”
“if P then Q”

Question 6

In a truth table a 0 means ___ and a 1 means _____

Answer 6

false
true

Question 7

what does this symbol mean ¬

Answer 7

not

Question 8

Tf the ¬ symbol applies to every letter in the statement

Answer 8

F, it only applies to the letter its directly touching

Question 9

what does logically equivalent mean

Answer 9

they have identical rows in a truth table

Question 10

given P⇒Q, Q⇒P is the ____

Answer 10

converse

Question 11

Given P⇒Q, what is the contrapositive statement

Answer 11

¬Q⇒¬P

Question 12

TF a conditional statement is only false when A is true and B is false

Answer 12

T, we only care about the antecedent(A) and consequence(B)

Question 13

TF a conditional statement is only violated when the antecedent is true but the consequent does not follow.

Answer 13

T

Question 14

what is P⇔Q

Answer 14

“P if and only if Q”
- means P and Q must have the same truth value then P⇔Q is true
- if they dont match then its false

Question 15

what is this symbol “∀”

Answer 15

The universal quantifier
“for all”
(∀x∈X)P(x): for all x in X, P(x)

Question 16

what is this symbol “∃”

Answer 16

The existential quantifier
“there exists”
(∃x∈X)P(x): there exists an x in X where P(x)