Propositions

Question 1

What is a proposition?

Answer 1

A statement which is either true or false

Question 2

What is a predicate

Answer 2

A statement that becomes a proposition, when a given free variable is defined

Question 3

What are the 2 universal quantifiers?

Answer 3

∀ (the universal quantifier) and ∃ (the ex- istential quantifier), which mean for all and there exists respectively. So

Question 4

what are propositional operators?

Answer 4

We can combine propositions by logical operations such as AND and OR. These are denoted by ∧ and ∨ respectively.

There is also the negation operator ¬ (NOT)

Question 5

What is the distributive identity for propositions?

Answer 5

P∨(Q∧R) = (P∨Q)∧(P∨R)

Question 6

What are de-morgans laws?

Answer 6

¬(P ∧ Q) = (¬P) ∨ (¬Q).

¬(P ∨ Q) = (¬P) ∧ (¬Q).

Question 7

How does negation work with propositions?

Answer 7

∀x∈R:x2 ≥0 goes to

∃x∈R:x2 <0,

Question 8

What is mathematical implication?

Answer 8

P ⇒ Q means P implies Q,

this means -
Q holds whenever P holds, or P implies Q.

Question 9

What are the three methods of proof

Answer 9

Direct proof, contrapositive and contradiction