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Discrete Mathematics
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Terms in this set (28)
Universal Statement
Is true for everything.
Eg. All animals are black.
Conditional Statement
If one thing is true then another thing is true too.
Eg. If 12 is divisible by 4 then it is divisible by 2.
P-->Q only false when P is true and Q is false.
Set Roster Notation
{1,2,3}
Set Builder Notation
{x ε s | P(x)}
A is a subset of B. Means what?
Every element in A is in B. Both have identical sets.
A is a proper subset of B. Means what?
Every element in A is in B but there is at least one element in B that is not in A.
Statement
A sentence that is true or false but not both.
Negation
Opposite.
Conjunction
P^Q
It is true only when both are true otherwise false.
Disjunction
P or Q
It is true if either P or Q is true. False when both are false.
Logically Equivalent
If two statements have identical truth tables.
De Morgan's Laws
The negations of "and" is "or" and vice versa.
Tautology
A statement that is true regardless of its truth values.
Contradiction
A statement that is false regardless of its truth values.
Contrapositive
Equivalent to a conditional statement "p-->q"
If ~q --> then ~p.
Converse
Not equivalent to a conditional statement.
If q--> then p.
Inverse
Not equivalent to a conditional statement.
If ~p then ~q.
"p only if q" means what?
"if not q then not p" or "if p then q."
Biconditional of p and q.
"p if, and only if q"
p<-->q
Only true if the both have the same truth values including if they both are false then they are true.
Negation Order
~
^
or
-->
<-->
Contradiction Rule
Say if p the statement is false and can prove it's contradiction then you can prove p is true.
Predicate
A statement with variables.
Eg. x^2=x
Domain
The set of all values that can be put in place of the predicate variables.
Eg.
predicate: x^2=x
domain: {x ε R}
Universal Quantifier
∀ "For all"
Existential Quantifier
∃ "There exists"
Universal Conditional Statement
∀, if p then q.
Negation of a Universal Conditional Statement
∀x, if P(x) then Q(x) ≡ ∃x such that P(x) and ∼Q(x)
Reciprocal of a real number a
is b so that ab=1
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