Geometry Help: Biconditionals and Definitions

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

Geometry Help: Measuring Segments and Angles

Geometry Help: Conditional Statements

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