unit 2

Question 1

what does 𝝆 represent in an if-then statement?

Answer 1

𝝆 represents the hypothesis, the “if” of an if-then statement.

Question 2

what does 𝓆 represent in an if-then statement?

Answer 2

𝓆 represents the conclusion, the “then” of an if-then statement.

Question 3

what does ~ (tilde) mean?

Answer 3

the ~ (tilde) means the “not”.

Question 4

what is a propositional statement?

Answer 4

a statement that can be true or false

Question 5

what is a counterexample?

Answer 5

a counterexample is a specific case that meets the hypothesis (𝝆) of a conditional statement.

Question 6

what does this symbol mean? ∴

Answer 6

this symbol means therefore

Question 7

what does this symbol mean? →

Answer 7

the arrow implies “if…, then…”

Question 8

what does this symbol mean? 🡘

Answer 8

this arrow means if and only if (biconditional)

Question 9

what does this symbol mean? ∧

Answer 9

this symbol means and, which is a conjunction.

Question 10

what does this symbol mean? ∨

Answer 10

this symbol means or, which is a disjucntion.

Question 11

conditional –

Answer 11

𝝆→զ
p implies q or if p, then q.

Question 12

converse –

Answer 12

զ→𝝆
q implies p or if q, then p.
(opposite!!)

Question 13

inverse –

Answer 13

~𝝆→~զ
not p implies not q or if not p, then not q.

Question 14

contropositive –

Answer 14

~զ→~𝝆
not q implies not p or if not q, then not p.

Question 15

biconditional –

Answer 15

𝝆 🡘 զ
p if and only if q

Question 16

when should biconditional be used?

Answer 16

only used if conditional and converse are both true

Question 17

law of detachment –

Answer 17

p→q
p
∴ q

Question 18

law of contropositive –

Answer 18

p→q
~q
∴~p

Question 19

law of syllogism –

Answer 19

p→q
q→r
p
∴r

Question 20

converse error –

Answer 20

p→q
q
∴p

Question 21

inverse error –

Answer 21

p→q
~p
∴~q

Question 22

what is a conjunction?

Answer 22

a conjunction is an intersection using the word “and”

Question 23

conjunction –

Answer 23

p ∧ q
p ∩ q

Question 24

when is a conjunction true?

Answer 24

a conjunction is true only when both parts are true.

Question 25

what is a disjunction?

Answer 25

a disjunction is a union using the word “or”.

Question 26

disjunction –

Answer 26

p ∨ q
p ∪ q

Question 27

when is a disjunction false?

Answer 27

a disjunction is false only when both parts are false.

Question 27

what is a universal set?

Answer 27

a universal set are integers from 1-10.