Propositional Logic and Set Notation Flashcards

1
Q

What is the meaning of ‘P ⇒ Q’?

A

P implies Q
or
If P then Q

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2
Q

When is ‘P∧Q’ true?

A

Only when BOTH P AND Q are true

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3
Q

When is ‘P∨Q’ true?

A

When either P OR Q are true

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4
Q

What does the symbol ‘¬’ mean?

A

Negation
turns true false and vice versa

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5
Q

What is the meaning of ‘P⇔ Q’?

A

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

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6
Q

What is a tautology?

A

A statement that is always true

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7
Q

What is the converse of ‘P ⇒ Q’?

A

Q⇒P

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8
Q

What is the meaning of ‘∀’?

A

For all…

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9
Q

What is the meaning of ‘∃’?

A

There exists…

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10
Q

What is the meaning of ‘∃!’?

A

There exists only 1…

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11
Q

What is the contrapositive of ‘P ⇒ Q’?

A

‘¬Q⇒¬P’
Not P implies not Q

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12
Q

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

A

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

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13
Q

Explain the set denoted by ℕ

A

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

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14
Q

Explain the set denoted by ℤ

A

Integers
{….-4,-3,-2,-1,0,1,2,3,4….}

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15
Q

Explain the set denoted by ℚ

A

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

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16
Q

Name the set denoted by ℝ

A

Real Numbers

17
Q

Name the set denoted by ℂ

A

Complex numbers

18
Q

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

A

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

19
Q

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

A

Closed interval from a to b, including a and b

20
Q

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

A

‘Clopen’ interval, including a but not b

21
Q

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

A

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

22
Q

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

A

A intersection B
{x : x∈A ∧ x∈B}

23
Q

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

A

A union B
{x : x∈A ∨ x∈B}

24
Q

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

A

{x : x∈A ∧ x∉B}

25
Q

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

A

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

26
Q

What is the meaning of A^c ?

A

Complement A, not A

27
Q

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

A

AxB= {(a,b): a∈A, b∈B}