Exercise 5: Logical Equivalence, Tautologies, and Applications

Covers testing logical equivalence, identifying the contrapositive of a conditional, verifying tautologies, and applying propositional logic to search-engine queries, program conditions, and combinatorial counting.

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Views #: 118

Questions #: 13

Time: 18 minutes

Pass Score: 80.0%

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Test an Equivalence of Compound Statements

1 pts

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Are (A ∧ B) ∨ C and A ∧ (B ∨ C) logically equivalent?

They are not equivalent

They are equivalent

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Identify the Contrapositive

1 pts

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Let P be the statement A → B. Is P logically equivalent to its converse, its inverse, or its contrapositive?

None

Converse

Inverse

Contrapositive

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Write a Search Query Excluding a Term

1 pts

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Write a logical expression for a web search engine to find sites about dogs that are not retrievers.

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Write a Search Query with OR and Exclusion

1 pts

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Write a logical expression for a web search engine to find sites about oil paintings by Van Gogh or Rembrandt, but not Vermeer.

"oil paintings" AND Van Gogh OR Rembrandt AND NOT Vermeer

"oil paintings" AND (Van Gogh OR Rembrandt) AND NOT Vermeer

oil paintings AND (Van Gogh OR Rembrandt) NOT Vermeer

"oil paintings" OR (Van Gogh AND Rembrandt) AND NOT Vermeer

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Write a Search Query Combining OR and AND

1 pts

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Write a logical expression for a web search engine to find sites about novels or plays about AIDS.

novels OR plays AND AIDS

(novels OR plays) AND AIDS

"novels" OR "plays" OR "AIDS"

novels AND plays AND AIDS

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Write a Search Query with a Geographic Exclusion

1 pts

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Write a logical expression for a web search engine to find sites about coastal wetlands in Louisiana but not in Alabama.

coastal wetlands AND Louisiana AND NOT Alabama

"coastal wetlands" OR Louisiana AND NOT Alabama

"coastal wetlands" AND Louisiana AND NOT Alabama

(coastal wetlands AND Louisiana) OR NOT Alabama

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Construct a Statement for Exclusive Conditions

1 pts

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Write a logical statement that is true only when exactly one of A or B is true (but not both), and C is false.

(A OR B) AND NOT C

(A AND B) AND NOT C

((A AND NOT B) OR (NOT A AND B)) AND NOT C

((A OR NOT B) AND (NOT A OR B)) AND NOT C

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Check Whether a Condition Matches Its Intended Meaning

1 pts

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Does the code condition "if not(A and B) and C" execute its statement only when A is false, B is false, and C is true?

Yes

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Verify an Implication Equivalence

1 pts

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Is A → B logically equivalent to A′ ∨ B?

Not Verified

Verified

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Negate a Real-World Conditional Statement

1 pts

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Write the negation of: If Sam passed his bar exam, then he will get the job.

If Sam did not pass his bar exam, then he will not get the job.

Sam passed his bar exam and he will not get the job.

Sam did not pass his bar exam and he will get the job.

If Sam gets the job, then he passed his bar exam.

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Count Memory Chip Configurations

1 pts

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A memory chip has 2⁵ ON-OFF elements. What is the total number of possible ON-OFF configurations of the chip?

\(2^(2^5)\)

\(2^5\)

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Match Each Input Pair to Its XOR Output

2 pts

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Input A	Input B	XOR Output
True (T)	True (T)	1($)
True (T)	False (F)	2($)
False (F)	True (T)	3($)
False (F)	False (F)	4($)

Match each pair of input truth values to the correct output of the exclusive OR (XOR).

Input A	Input B	XOR Output
True (T)	True (T)	(1)
True (T)	False (F)	(2)
False (F)	True (T)	(3)
False (F)	False (F)	(4)

Please drag and drop the selected option in the right place or type it instead

False

True

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Prove an XOR Equivalence

1 pts

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Is A XOR B ↔ (A ↔ B)′ a tautology?

Proven

Not Proven

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Year 11 Year 12

Test an Equivalence of Compound Statements

Correct Answer

Explanation

Identify the Contrapositive

Correct Answer

Explanation

Write a Search Query Excluding a Term

Correct Answer

Explanation

Write a Search Query with OR and Exclusion

Correct Answer

Explanation

Write a Search Query Combining OR and AND

Correct Answer

Explanation

Write a Search Query with a Geographic Exclusion

Correct Answer

Explanation

Construct a Statement for Exclusive Conditions

Correct Answer

Explanation

Check Whether a Condition Matches Its Intended Meaning

Correct Answer

Explanation

Verify an Implication Equivalence

Correct Answer

Explanation

Negate a Real-World Conditional Statement

Correct Answer

Explanation

Count Memory Chip Configurations

Correct Answer

Explanation

Match Each Input Pair to Its XOR Output

Correct Answer

Explanation

Prove an XOR Equivalence

Correct Answer

Explanation

Quran Recitation

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