Lecture notes

Question 1

Statement

Answer 1

a sentence which is either true or false, but not both

Question 2

not(P or Q) is equivalent to

Answer 2

not(P) and not(Q)

Question 3

not(P and Q) is equivalent to

Answer 3

not(P) or not(Q)

Question 4

converse of P =⇒ Q

Answer 4

Q =⇒ P

Question 5

contrapositive of P =⇒ Q

Answer 5

(not Q) =⇒ (not P)

Question 6

“not(P =⇒ Q)” is equivalent to

Answer 6

“P and not(Q)”

Question 7

Triangle inequality

Answer 7

For all x, y ∈ R, |x + y| ≤ |x| + |y|

Question 8

Symbolically, the set A ⊆ R is bounded above if and only if

Answer 8

∃M ∈ R s.t. ∀a ∈ A, a ≤ M

Question 9

A is bounded below if and only if

Answer 9

∃m ∈ R s.t. ∀a ∈ A, m ≤ a

Question 10

Let A ⊆ R. Then A is bounded if and only if

Answer 10

∃K > 0 s.t. ∀a ∈ A, |a| ≤ K