knowverseTruth tables list every possible combination of truth values for a compound statement and show the resulting value for each possible assignment. The quiz covers conjunction, inclusive or, conditional statements, tautology and contradiction in propositional logic. Try the ten questions and see how you do.
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A proposition is defined as a claim that possesses a definite truth value of either true or false.
In logic, we call a statement that is either true or false a proposition.
From the Knowverse course text.
A false mathematical statement still has a truth value. Commands and questions do not assert propositions.
Even though that statement is mathematically wrong, it is still a proposition with a 'False' truth value.
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Double negation flips a truth value twice, returning it to its original state.
In logic, two negatives always cancel each other out and return you to the original statement.
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A conjunction is false if even one component is false; every statement joined by 'And' must be true.
A conjunction acts like a strict judge who only accepts the total truth.
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Logical disjunction is inclusive, meaning it evaluates as true whenever at least one component, or both, is true.
Inclusive means that the statement works if the first part is true, the second part is true, or both are true.
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The antecedent is the proposition following if. The consequent follows then. A logical conditional does not by itself establish a causal mechanism.
In logic, this first part is called the antecedent. The antecedent is the 'if' portion that must be true for the rest of the statement to matter.
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A tautology is a logical structure that remains true under every single potential condition.
In logic, we call a statement that is true in every possible case a tautology.
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A contradiction contains opposing elements that guarantee it evaluates as false in every scenario.
A statement that is always false, no matter what, is called a contradiction.
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Universal quantification applies to an entire set without exception; a single counter-example makes it false.
For a Universal Quantifier to be true, every single individual must satisfy the property being discussed.
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A truth table checks all possible truth-value combinations.
A truth table is simply a map that shows every possible combination of truth and falsity for our statements.
From the Knowverse course text.
See the answer and explanation for each question below.
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Classical propositional logic studies statements that have a truth value, either true or false. A false claim still qualifies. 'Ten is less than two' makes a claim with a clear truth value, while a command such as 'Close the door' asks someone to act rather than asserting something true or false.
Logical operators combine or change those truth values. Negation reverses one, and applying it twice restores the original. A conjunction, written with 'and', is true when both parts are true. An inclusive 'or' is true when at least one part is true, including when both are true.
In logic, we call a statement that is either true or false a proposition.
From the Knowverse course text.
A truth table lists the possible combinations of truth values and the result for a compound statement. It helps distinguish a tautology, true under every assignment, from a contradiction, false under every assignment. A conditional has an antecedent after 'if' and a consequent after 'then'. Those names identify the two parts.
Quantifiers say how widely a claim applies within a stated domain. A universal claim applies to every member, so a counterexample defeats it. An existential claim needs at least one matching case. Keeping the domain clear matters when deciding which examples count and whether a claim has actually been established.
The antecedent is the 'if' portion that must be true for the rest of the statement to matter.
From the Knowverse course text.
Sources: The Language of Truth. Each question or step includes an excerpt from the course.
