Connectives and truth tables
Propositions, truth values and connectives (not, and, or, exclusive or, implication, equivalence): reading a table, translating a sentence into a formula and spotting tautologies and contradictions.
- 24 cards
- 5 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- The numbers
- Scenarios
A few cards from the deck
Proposition: what is it?
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A statement that can be said without ambiguity to be true or false, such as "7 is a prime number".
"Close the door!" or "x > 3" (while x has no value) are not: no truth value is attached to them.
In which single case is "p or q" (∨) false?
- p false and q false
- p true and q true
- p true and q false
- p false and q true
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p false and q false
An inclusive or is true as soon as one of the two is true, including when both are. It is false only on the (false, false) row.
Out of the four rows of its table, "p and q" (∧) is … on …: the row where p and q are both true.
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Out of the four rows of its table, "p and q" (∧) is true on only one: the row where p and q are both true.
One false side is enough to make the "and" false. The ∨, for its part, is inclusive: it stays true when both are, unlike the "soup or salad" of a restaurant menu.
Logical connective: what is it?
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An operator that builds a proposition from one or two others, whose value depends only on their values: ¬, ∧, ∨, ⇒, ⇔.
That is what lets a table describe everything: knowing the values of the pieces is enough to know the value of the whole.