phone
p ~p
T
F
p q p ∧ q
T T
T F
F T
F F
p q r p ∧ q ∧ r
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
mammal a cat.

Logic Evaluation

Instructions: When you have finished the evaluation, click the "Submit Answers" button at the bottom of the page. Note: some questions may have more than one possible answer.

  1. Which of the following does NOT describe a logical statement?
    1. It declares something.
    2. It must be true or false, but not both.
    3. It can be an opinion.
    4. It has a truth value.
  2. Negate this statement: Every cat is a mammal.
    cat a mammal.
  3. Which of these is NOT a connective
    1. and
    2. or
    3. might
    4. not
  4. Let p = Today is Tuesday
    q = The time is 8am

    Write this symbolic statement in plain English: (~p) ∧ q

  5. Let p = Today is Wednesday
    q = N & S College is open

    Write this English statement in symbols:

    Today is Wednesday but N & S College is not open.

file
Glossary

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Daycart Local News

At Least One Fatality Considered in Arson Case

#AtLeastOneDead

Local police thought every resident had evacuated the buildings during the recent fires. It turns out they were wrong - at least one resident had not evacuated- as they discovered when what looks to be a burned body turned up in the rubble.

(Click for audio)

Law Student to Assist in Crime-Fighting

#DiekoDruvall

Local pre-law student Dieko Druvall (who goes by the nickname "Dee") has won the recent contest to identify logical thinkers to assist with the wave of local crimes. She will be "riding along" with revered Detective Natazda Braxton, daughter of Lisa Braxton, who gained fame as the first black woman to serve as Chief of Police in the island town of Daycart.

We got a quote from Dieko Druvall at the local police station:

    - Dieko Druvall

Dieko was one of the residents in the dorm that caught fire last night, and is rumored to have suffered a bump to the head from falling debris. A concussion is suspected, and it is unclear whether this will affect her performance in the crime assistantship, or even result in cancelling the program.

(Click for audio)

Some Sugars Cause Cancer

#SomeSugarsDo

I know what you're thinking: "No way. No sugars cause cancer." But I'll negate that right now. Some sugars cause cancer...

(Click for audio)

Op Ed: Zaina Needs to Resign-uh

#ZainaScrewedUs

Everyone likes Zaina Roux, right? Wrong, somebody does not like her. I know this because I do not like her. The popular CFO of Y & Z Industries did not warn us investors about the likelihood of the Bitpence gamble's negative impact on our stock prices. If any of these were true, I'd be happy:

  1. She ran a press release.
  2. She told everyone about it.

But they are not true. Their negations are true:

  1. She did not run a press release.
  2. There is at least one person she didn't tell about it.

I know this last one, because she DIDN'T. TELL. ME. And now I'm much poorer, and much angrier.

Bitter and worse,
Claudio P.
(submitted on June 20)

(Click for audio)

Glossary

antecedent

The statement A of a compound statement that can be written in the form "if A then B"

urbane_lexicon.com:
    Dat firrrst part of an "if, then" statement

argument

A logical deduction where statements are used to support a final statement. The argument has the form

Also see "premise", "conclusion", "valid".

urbane_lexicon.com:
    Like, when ya girl be like "this" and "that" and "whatever" means "some shit", and you're sitting there trying to figure out if she's right.

biconditional A compound statement of the form "[statement 1] if and only if [statement 2]". This is only true when statement 1 and statement 2 are both true or both false. It is equivalent to the compound statement "if [statement 1] then [statement 2] and if [statement 2] then [statement 1]".

urbane_lexicon.com:
    Some "if and only if" situation. Like "I smoke weed if and only if it's a day that ends in Y." Got it? If I'm gettin high, then today ends in Y, and if today ends in "Y" I'm getting high.

case For the symbolic logic, we use "case" to refer to every combination of truth values for a given set of simple statements. For example, if we have two statements, p and q, then we have 4 cases to consider: (1) p is true and q is true (2) p is true and q is false (3) p is false and q is true (4) p is false and q is false

urbane_lexicon.com:
    All possibilities. Like for two things: Yes yes. Yes no. No yes. No no.

urbane_lexicon.com:
    See "compound statement"

compound statement A statement consisting of one ore more simple statements, along with connective term(s) acting on the statement(s).

urbane_lexicon.com:
    Yapping about more than one thing, all at the same time.

conclusion The final statement in an argument.

urbane_lexicon.com:
    The [some shit] of an argument.

conditional A compound statement that can be written in the form "if [statement 1] then [statement 2]". This is only false when statement 1 is true but statement 2 is false.

urbane_lexicon.com:
    some "if, then" statement

conjunction A compound statement combining two statements with "and" or "but".

urbane_lexicon.com:
    Like when a girl is like "I want dinner AND a movie", or I'm like "You get dinner BUT no movie"

connective A word or phrase that acts on or connects statements. Examples: "and", "or", "not", "if... then", "if and only if".

urbane_lexicon.com:
    some word piecing shit together: "and", "or", "not", "if... then", "if and only if".

consequent If a compound statement that can be written in the form "if [statement 1] then [statement 2]", then [statement 2] is the consequent.

urbane_lexicon.com:
    Dat second part of an "if, then" statement

contradiction A compound statement that is false in every case.

urbane_lexicon.com:
    Always wrong, like you (to your girlfriend).

contrapositive For a conditional statement of the form "if [statement 1] then [statement 2]", the contrapositive is the statement "if [statement 1] then [statement 2]". This is equivalent to the conditional.

urbane_lexicon.com:
    Changing an "if this then that" statement to "if not that then not this." So, "If I have beer, then I am drinking." becomes "If I'm not drinking, then I don't have beer." Guess what, those two are equivalent. Whoa, mind blown.

converse For a conditional statement of the form "if [statement 1] then [statement 2]", the converse is the statement "if [statement 2] then [statement 1]". This is not equivalent to the conditional, however it is equivalent to the inverse.

urbane_lexicon.com:
    Turning and "if, then statement" around. "If I live in Los Angeles then I live in California." becomes "If I live in California then I live in L.A." That shit don't even make sense, here. Not equivalent to the first statement..

De Morgan's Laws The two laws (used in logic, math, computer science, set theory, and other fields) that say: if you distribute "not" over an "and" or "or" statement, then you must change that connective to the other one: not(p and q) ≡ not p or not q; not(p or q) ≡ not p and not q

urbane_lexicon.com:
    if it's not this or that, then it's not this AND not that. Not this and that? Then it's not this OR not that.

dysjunction A compound statement combining two statements with "or".

urbane_lexicon.com:
    Like when a girl is all "You can buy me dinner OR you can go home." You think you got two options, but yo, if you piss her off after you buy dinner, guess what, you are STILL going home.

equivalent Having the same truth value in every case. You can show that two statements are equivalent, but putting each as a column into the same truth table. If all the truth values in their columns match up exactly, they are equivalent.

urbane_lexicon.com:
    Each is true where the other is true, and each is false where the other is false. Like when I cheat off the smart kid's True/False quiz in class. Our answers are both True and False in all the same places. So how come he gets an A and I get an F for cheating???

exclusive or The "or" common in plain English, that indicates "one or the other, but NOT both".

urbane_lexicon.com:
    Like that awkward moment when you have to decide if you will go hook up with your girlfriend or boyfriend tonight, because you're bi but neither one of them is.

existential quantifier A quantifier relating to whether a least one of something exists: "some", "at least one", "there exists"

urbane_lexicon.com:
    " sometin' ". " err-tin' ". " at least one-tin' ". Words like that.

fallacy An invalid argument.

urbane_lexicon.com:
    A man's attempt at an argument. That's why it sounds like "phallus". (not really)

inclusive or The usual logical "or", which includes cases "one or the other or both"; see definition for "or"

urbane_lexicon.com:
    Like when you're at a bar and hoping to go home with that blonde or that brunette, but fuck if you would say no to going home to both.

invalid Not valid.

urbane_lexicon.com:
    When you find some specific case that breaks down your girl's argument, and she gives you the death stare and you're like "fuck, what have I done..."

inverse For a conditional statement of the form "if [statement 1] then [statement 2]", the inverse is the statement "if not [statement 1] then not [statement 2]". This is not equivalent to the conditional, however it is equivalent to the converse.

urbane_lexicon.com:
    Adding "not"s to each part of an "if, then statement". "If I live in Los Angeles then I live in California." becomes "If I don't live in L.A. then I don't live in California" What the hell, yo- but I live in San Fran! This shit is not equivalent to the first statement..

logic A branch of science studying correct reasoning and deduction.

urbane_lexicon.com:
    gettin smart

negate To form a statement from an original statement, where the new statement has the opposite truth value in every case.

urbane_lexicon.com:
    To turn something into its negation. Often used when talking shit with someone.

negation A similar statement that has the opposite truth value in every possible situation.

urbane_lexicon.com:
    Something that flips your statement upside down. True becomes false and false becomes true, yo.

premise An assumption, law, clue, etc. used to build an argument.

urbane_lexicon.com:
    The [this], [that], [whatever] part of an argument.

proposition See "simple statement"

urbane_lexicon.com:
    See "statement"

quantified statement see "quantifier"

urbane_lexicon.com:
    A statement with a quantifier, duh

quantifier Something that describes the amount of something that exists. A statement containing a quantifier is sometimes called a "quantified statement".

urbane_lexicon.com:
    Something telling you like, "How much is that?"

simple statement A statement that cannot be broken down into smaller logical statements without losing meaning. Sometimes called a "proposition".

urbane_lexicon.com:
    Like, saying the most basic of the basic.

statement A complete, declarative sentence that is true or false but not both simultaneously.

urbane_lexicon.com:
    Something that's legit or bunk, but no both.

symbolic logic The formal study of logic that uses symbols to represent statements and the phrases that connect them.

urbane_lexicon.com:
    Logic with symbols. Like algebra, but with words or something.

tautology A compound statement that is true in every case.

urbane_lexicon.com:
    Always right, like your girlfriend.

truth table A table containing a row for each case for a compound statement, showing what the resulting truth value will be of that compound statement in each case.

urbane_lexicon.com:
    A table of cases... a way to visualize how the truth values come together for some statements. Fucking wild.

truth value true or false, often written as T or F, respectively

urbane_lexicon.com:
    "true" or "false". Like, "Becky-- You like me. Check the truth value below.
            T []   F []"

universal quantifier A quantifier relating to whether or not every given item falls into some case: "all", "every", "none", "nobody", etc.

urbane_lexicon.com:
    Words like "errry-one", "all dat", "nothin' at all", you know...

valid An argument is valid if it is true whenever each of its premises is assumed to be true.

urbane_lexicon.com:
    When ya girl turns out to be right, because (you assume) [this], [that], and [whatever] were right.

XOR exclusive or

urbane_lexicon.com:
    exclusive or. Said like "ex or". Like "Would you like to be my ex or are you gonna stop being a twat?"

Symbols

Symbol Translation
~ not
∧ and
∨ or
→ if... then
↔ if and only if
⊕ or ⊻ xor ("exclusive or")
≡ is (logically) equivalent to

Contacts

Contact Phone Added
Ada Vici
(Assist. DA) 		555-VICI 1 yr
Anne
(admin) 		555-DESK 1 mo
Cory 555-CORY 6 mo
お母さん
(Mama) 		+81+
555-MAMA 		> 5 yr
Dad 555-PAPA > 5 yr
Jojo 555-JOJO > 2 yr
Manesh
(Cryptographer) 		555-MANS 2 wk
Natazda Braxton
(Detective) 		555-COPS 2 wk
Simon 555-SIMO < 1 wk
Soo-yun 555-SYUN 2 yr
Tara 555-TARA 1 mo

Settings

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"statement" added...

(... what does his response mean...? We can only check ONE of these as the correct answer...)

You can lead a horse to water or you can't make him drink, but you can take a horse to school and you can't make him think.

You can lead a horse to water or you can make him drink, and you can take a horse to school but you can't make him think.

You can lead a horse to water or you can make him drink, or you can take a horse to school but you can't make him think.

Universal quantifiers: are negated by
Existential quantifiers:
All cats are tigers.
(Every cat is a tiger.) 		Some cats are not tigers.
(At least one cat is not a tiger.)
(There exists a cat that is not a tiger.)
No cat is a tiger.
(No cats are tigers.) 		Some cats are tigers.
(At least one cat is a tiger.)
(There exists a cat that is a tiger.)
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