Topic 1 - Basic Concepts

Question 1

Define: Conjunction

Answer 1

A statement that is true if and only if both statements P and Q are true, denoted P ∧ Q

Question 2

Define: Disjunction

Answer 2

A statement that is true if and only if either statements P or Q (or both) are true, denoted P ∨ Q.

Question 3

Define: Negation

Answer 3

A statement that has the opposite truth value to that of P, denoted ¬P.

Question 4

Define: Implication

Answer 4

A statement compounded by two statements (P and Q) of the form “if P…, then Q…”, denoted P ⇒ Q.

Question 5

Define: Equivalence

Answer 5

A statement compounded by two statements (P and Q) such that P ⇒ Q and Q ⇒ P, denoted P ⇔ Q

Question 6

Define: Set

Answer 6

A collection of distinct objects, called elements

Question 7

Define: Function

Answer 7

A rule that assigns each element of a set A a unique element of a set B, denoted f: A → B.

Question 8

T/F: The negation of “P ∧ Q” is “¬P ∨ ¬Q”.

Answer 8

True. The negation of “P ∧ Q” is “¬(P ∧ Q)”, which is equivalent to “¬P ∨ ¬Q” by De Morgan’s Law.

Question 9

T/F: (P∧Q) ⇒ R is equivalent to ¬(P∧Q) ⇒ ¬R.

Answer 9

False. It is equivalent to ¬R ⇒ ¬(P∧Q) by the contrapositive proposition.