Section 2.1

Question 1

Statement

Answer 1

A statement (or proposition) is a sentence that is true or false but not both.

Question 2

Negation of p

Answer 2

The negation of p is “not p” or “it is not the case that p”

Denoted ~p

Has the opposite truth value from p: if p is true, ~p is false and vice versa

Question 3

Conjunction

Answer 3

If p and q are statement variables:

The conjunction of p and q is “p and q,” denoted p^q.

p^q is true only when BOTH p and q are true. If either or both statement variables are false, p^q is false.

Question 4

Disjunction

Answer 4

If p and q are statement variables:

The disjunction of p and q is “p or q,” denoted p v q.

It is true when either p is true or q is true or both are true. It is false only when BOTH p and q are false.

Question 5

Statement form

Answer 5

A statement form (or propositional form) is an expression made up of statement variables (such as p, q, and r) and logical connectives (such as ~, ^, and v) that becomes a statement when actual statements are substituted for the component statement variables.

The truth table for a given statement form displays the truth values that correspond to all possible combinations of truth values for its component statement variables.

Question 6

Logically equivalent

Answer 6

Two statement forms are logically equivalent if and only if they have identical truth values for each possible substitution of statements for their statement variables.

Logical equivalence of statement forms P and Q is denoted P≡Q

Two statements are logically equivalent if and only if they have logically equivalent forms when identical component statement variables are used to replace identical component statements.

Question 7

De Morgan’s Laws

Answer 7

The negation of an and statement is logically equivalent to the or statement in which each component is negated.

The negation of an or statement is logically equivalent to he and statement in which each component is negated.

Question 8

Tautology

Answer 8

A statement form that is always true regardless of the truth values of the individual statements substituted for its statement variables.

A statement whose form is a tautology is a tautological statement

Question 9

Contradiction

Answer 9

A statement form that is always false regardless of the truth values of the individual statements substituted for its statement variables.

A statement whose form is a contradiction is a contradictory statement.