Term
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Definition
a statement that can be written in the form “If p, then q,” where p is the hypothesis and q is the conclusion
Example: If a vehicle is a long board, then the vehicle has four wheels. |
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| hypothesis (of a conditional statement) |
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Definition
| the clause following the words “if a(n)” in a conditional statement |
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| conclusion (of a conditional statement) |
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Definition
| the clause following the words “then the” in a conditional statement |
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Term
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Definition
| A diagram composed of closed shapes used to illustrate the logical relationship among sets of objects. It is useful for illustrating conditional statements. |
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Term
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Definition
| an object that proves a conditional statement false. The object must fit the hypothesis but not the conclusion. |
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Term
| converse (of a conditional statement) |
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Definition
| a conditional statement formed by switching the hypothesis and conclusion of a conditional statement. An original statement “If p then q” becomes “If q then p” |
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Term
| biconditional (statement) |
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Definition
a conditional statement that is true both “forward” and “backward” and is written using “Iff” or “If and only if”
Example:
"A quadrilateral is a rectangle if and only if it has four right interior angles" or "Iff a quadrilateral is a rectangle, then it has four right interior angles." |
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Term
| inverse (of a conditional statement) |
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Definition
| a conditional statement formed by negating both the hypothesis and conclusion of a conditional statement. An original statement “If p then q” becomes “If not p then not q.” |
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Term
| contrapositive (of a conditional statement) |
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Definition
| a conditional statement formed by first negating both the hypothesis and conclusion of a conditional statement and then switching them. An original statement “If p then q” becomes “If not q then not p.” This form of a true conditional statement is always true. |
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