Discrete Math test 1

Statement

a declarative sentence that is either true or false, not both, not neither.

Is “I am not lying“ a statement?

No

Is “Today is Thursday“ a statement?

True

Open sentence

a declarative sentence whose true/falseness depends on the value of one or more variables. (Not a statement)

Domain of an open sentence

is the set of values the variables could take.

“Not”

~ negation

“And”

∧ conjunction

“Or”

V disjunction

Truthtable

gives all possible truth values for a statement given those of its components.

Two compound statements R & S constructed from the same component statements are logically equivalent

if R & S have the same truths values for all component truth values combos. “R≡S“

DeMorgan’s Law

For every statement P & Q,

~(PVQ)≡(~P)∧(~Q)

~(P∧Q)≡(~P)V(~Q)