Exercise 6: Functional Completeness, Multi-Valued Logic, and Logic Puzzles

Covers which sets of logical connectives are functionally complete, extending truth tables to three-valued logic, and solving classic self-referential logic puzzles.

download Export

search_insights Statistics

stylus_note White Board

Quran

calculate Calculator

dictionary Dictionary

fullscreen Full Screen

more_vert More

QUESTION OF

volume_mute Read quiz aloud

Views #: 108

Questions #: 14

Time: 20 minutes

Pass Score: 80.0%

Style

Step

List

Mode

Exam

Practice

Test Functional Completeness of {AND, NOT}

1 pts

volume_mute

Is every compound statement equivalent to one built using only AND and NOT?

Not Proven

Proven

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Test Functional Completeness of {OR, NOT}

1 pts

volume_mute

Is every compound statement equivalent to one built using only OR and NOT?

Not Proven

Proven

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Test Functional Completeness of {IMPLIES, NOT}

1 pts

volume_mute

Is every compound statement equivalent to one built using only IMPLIES and NOT?

Not Proven

Proven

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Test Functional Completeness of {IMPLIES, OR}

1 pts

volume_mute

Are there compound statements that are NOT equivalent to any statement built using only IMPLIES and OR?

Not Proven

Proven

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Test Functional Completeness of NAND (Sheffer Stroke)

1 pts

volume_mute

Is every compound statement equivalent to one built using only the NAND connective?

Not Proven

Proven

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Test Functional Completeness of NOR (Peirce Arrow)

1 pts

volume_mute

Is every compound statement equivalent to one built using only the NOR connective?

Proven

Not Proven

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Count Rows in a Three-Valued Truth Table

1 pts

volume_mute

In a three-valued logic system, how many rows are needed for a truth table with n statement letters?

\(2^n\)

\(3n\)

\(3^n\)

\(n^3\)

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Identify the Missing Case in the "Known Knowns" Quote

1 pts

volume_mute

In a well-known 2002 remark, Secretary of Defense Donald Rumsfeld distinguished "known knowns," "known unknowns," and "unknown unknowns." Which of the four combinations of knowing/not-knowing whether we know something did he leave out?

Unknown knowns

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Analyze an Ambiguous Advertisement

1 pts

volume_mute

A club's advertisement reads: "Members and nonmembers only." Because "and" is being used to combine two mutually exclusive categories, the statement can genuinely be read in more than one way. Select every correct interpretation.

Read inclusively (as “member or nonmember”), the statement applies to everyone, since every person is either a member or a non-member - making it a tautology.

The statement is a completely unambiguous restriction that applies only to paying members.

Read literally as requiring both categories at once, the statement applies to no one, since nobody can be a member and a non-member simultaneously - making it an empty, impossible condition.

The statement only applies to people who have applied for membership but have not yet been approved.

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Analyze the Liar Paradox

1 pts

volume_mute

A person says only "I am a liar." Can any consistent conclusion be reached about whether this statement is true or false?

Yes

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Determine the true identities of Percival and Llewellyn

1 pts

volume_mute

Percival and Llewellyn are from a land where everyone is either a truth-teller or a liar. Percival says, "At least one of us is a liar."

Both Percival and Llewellyn are truth-tellers

Percival is a liar, and Llewellyn is a truth-teller

Both Percival and Llewellyn are liars

Percival is a truth-teller, and Llewellyn is a liar

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Determine the true identities of Merlin and Meredith

1 pts

volume_mute

Merlin and Meredith are from a land where everyone is either a truth-teller or a liar. Merlin says, "If I am a truth-teller, then Meredith is a truth-teller."

Both Merlin and Meredith are truth-tellers

Merlin is a truth-teller, and Meredith is a liar

Merlin is a liar, and Meredith is a truth-teller

Both Merlin and Meredith are liars

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Determine the true identities of Rothwold and Grymlin

1 pts

volume_mute

Rothwold and Grymlin are from a land where everyone is either a truth-teller or a liar. Rothwold says, "Either I am a liar, or Grymlin is a truth-teller."

Both Rothwold and Grymlin are truth-tellers

Rothwold is a truth-teller, and Grymlin is a liar

Rothwold is a liar, and Grymlin is a truth-teller

Both Rothwold and Grymlin are liars

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Determine the true identities of Gwendolyn and Merrilaine

1 pts

volume_mute

Gwendolyn and Merrilaine are from a land where everyone is either a truth-teller or a liar. Gwendolyn says, "I am a liar, but Merrilaine is not."

Both Gwendolyn and Merrilaine are truth-tellers

Gwendolyn is a truth-teller, and Merrilaine is a liar

Gwendolyn is a liar, and Merrilaine is a truth-teller

Both Gwendolyn and Merrilaine are liars

note_alt Add notes

flag Flag

volume_mute

Correct Answer

Explanation

Year 11 Year 12

Test Functional Completeness of {AND, NOT}

Correct Answer

Explanation

Test Functional Completeness of {OR, NOT}

Correct Answer

Explanation

Test Functional Completeness of {IMPLIES, NOT}

Correct Answer

Explanation

Test Functional Completeness of {IMPLIES, OR}

Correct Answer

Explanation

Test Functional Completeness of NAND (Sheffer Stroke)

Correct Answer

Explanation

Test Functional Completeness of NOR (Peirce Arrow)

Correct Answer

Explanation

Count Rows in a Three-Valued Truth Table

Correct Answer

Explanation

Identify the Missing Case in the "Known Knowns" Quote

Correct Answer

Explanation

Analyze an Ambiguous Advertisement

Correct Answer

Explanation

Analyze the Liar Paradox

Correct Answer

Explanation

Determine the true identities of Percival and Llewellyn

Correct Answer

Explanation

Determine the true identities of Merlin and Meredith

Correct Answer

Explanation

Determine the true identities of Rothwold and Grymlin

Correct Answer

Explanation

Determine the true identities of Gwendolyn and Merrilaine

Correct Answer

Explanation

Quran Recitation

Query Dictionary

Select a result: