M1 Topic 2: Propositions

Question 1

A declarative statement which is true or false, but not both. Lowercase letters such as p, q, r, and s are used to represent simple propositions

Answer 1

Proposition (or statement)

Question 2

The study of how simple propositions can come together to make more complicated propositions

Answer 2

Propositional logic

Question 3

The attribute assigned to a proposition depending on its truthfulness or falsehood, which in classical logic has only two possible values (true or false)

Answer 3

Truth value

Question 4

In Propositional Logic, we assume a collection of simple or atomic propositions are given:

Answer 4

p, q, r, s, t, ….

Question 5

Then we form compound propositions by using logical connectives (logical operators) to form ______

Answer 5

propositional “molecules”

Question 6

A mathematical table showing how truth or falsity of a proposition varies with that of its components

Answer 6

truth table

Question 7

Interpreted intuitively as being true when p is false and false when p is true

Answer 7

Negation (¬p)

Question 8

What happens when we use the word “and” in English. If one is false, then the compound statement is false as well.

Answer 8

Conjunction (p∧q)

Question 9

The use of “or”. It is true when at least one of the two propositions is true.

Answer 9

Disjunction (p∨q)

Question 10

Usage of “if, then” or “implies”. p → q is false only if p is true while q is false

Answer 10

Conditional/Implication (p→q)

Question 11

p is called the ______ (or antecedent or premise) under Conditional/Implication

Answer 11

hypothesis

Question 12

q is called the ______ (or consequence) under Conditional/Implication

Answer 12

conclusion

Question 13

Ways to express the conditional statement p→q:

Answer 13

1. If p then q
2. p implies q
3. If p, q
4. p only if q
5. p is sufficient for q

Question 14

Some of the ways reverse the order of p and q but have the same connotation i.e. p→q:

Answer 14

1. q if p
2. q whenever p
3. q is necessary for p

Question 15

Is read as “p if and only if q”. For p↔q to be true, p and q must have the same truth values. Otherwise, p↔q is false

Answer 15

Bi-conditional/Double Implication (p↔q)