Propositional Logic and Set Notation

Question 1

What is the meaning of ‘P ⇒ Q’?

Answer 1

P implies Q
or
If P then Q

Question 2

When is ‘P∧Q’ true?

Answer 2

Only when BOTH P AND Q are true

Question 3

When is ‘P∨Q’ true?

Answer 3

When either P OR Q are true

Question 4

What does the symbol ‘¬’ mean?

Answer 4

Negation
turns true false and vice versa

Question 5

What is the meaning of ‘P⇔ Q’?

Answer 5

P if and only if Q
or
P is sufficient and necessary for Q

Question 6

What is a tautology?

Answer 6

A statement that is always true

Question 7

What is the converse of ‘P ⇒ Q’?

Answer 7

Q⇒P

Question 8

What is the meaning of ‘∀’?

Answer 8

For all…

Question 9

What is the meaning of ‘∃’?

Answer 9

There exists…

Question 10

What is the meaning of ‘∃!’?

Answer 10

There exists only 1…

Question 11

What is the contrapositive of ‘P ⇒ Q’?

Answer 11

‘¬Q⇒¬P’
Not P implies not Q

Question 12

What can be said about a statement based on its contrapositive?

Answer 12

A statement is true, if and only if, its contrapositive is true.

Question 13

Explain the set denoted by ℕ

Answer 13

Natural numbers
aka the counting numbers
{1,2,3,4,5,6……}

Question 14

Explain the set denoted by ℤ

Answer 14

Integers
{….-4,-3,-2,-1,0,1,2,3,4….}

Question 15

Explain the set denoted by ℚ

Answer 15

Rational numbers
set of a/b, where a is an integer, and b is natural

Question 16

Name the set denoted by ℝ

Answer 16

Real Numbers

Question 17

Name the set denoted by ℂ

Answer 17

Complex numbers

Question 18

What is the meaning of the interval notation
(a,b) or ]a,b[

Answer 18

Open interval from a to b, not including a or b

Question 19

What is the meaning of the interval notation
[a,b]

Answer 19

Closed interval from a to b, including a and b

Question 20

What is the meaning of the interval notation
[a,b[

Answer 20

‘Clopen’ interval, including a but not b

Question 21

What is the meaning of builder notation,
{x : P(x)} ?

Answer 21

The set of x, subject to some condition P(x)

Question 22

What does A∩B mean? And how can it be expressed in builder notation?

Answer 22

A intersection B
{x : x∈A ∧ x∈B}

Question 23

What does A∪B mean? And how can it be expressed in builder notation?

Answer 23

A union B
{x : x∈A ∨ x∈B}

Question 24

What does A\B mean? And how can it be expressed in builder notation?

Answer 24

{x : x∈A ∧ x∉B}

Question 25

What does A⊂B mean? And how can it be expressed?

Answer 25

A is a subset of B or A is contained in B
x∈A ⇒ x∈B

Question 26

What is the meaning of A^c ?

Answer 26

Complement A, not A

Question 27

What is the cartesian product (AxB)of two sets A, B?

Answer 27

AxB= {(a,b): a∈A, b∈B}