Geometry Help: Biconditionals and Definitions
Published by Discovering how to write a biconditional and what a good definition is.
Biconditionals
Biconditional statements, or “if and only if” statements, are reversible. They are written as P↔Q and read as “if and only if”.
Example 1
Determine if Biconditional or not.
A) If x=3, then x²=9
P→Q – x=3 → x²=9 – True
Q→P – x²=9 → x=3 – False (x=3, x=-3)
Not biconditional
B) If it is December 25, then it is Christmas Day.
P→Q – It is December 25 → It is Christmas Day – True
Q→P – It is Christmas Day → It is December 25 – True
Biconditional
Definitions
Definitions must be precise and must be reversible.
If And Only If
iff stands for “if and only if”
Example 2
Determine if it’s a ”good definition”. If it is, write the biconditional.
A) Parallel lines don’t intersect. – No (skew lines)
B) Parallel planes don’t intersect.- Yes…Write Biconditional.
Planes are parallel iff (if and only if) they don’t intersect.
Further Reading
Geometry Help: Points, Lines, and Planes
Geometry Help: Segments, Rays, Parallel Lines, and Planes
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