Question

decide if this biconditional statement is true or false. a point is the origin if and only if its coordinates are both zero. false true

Explanation:

Step1: Analyze the forward implication

If a point is the origin, by definition, its coordinates are \((0,0)\).

Step2: Analyze the reverse implication

If a point has coordinates \((0,0)\), by the definition of the origin in the coordinate system, it is the origin.
Since both the forward (\(p\Rightarrow q\)) and reverse (\(q\Rightarrow p\)) implications are true for \(p\): "A point is the origin" and \(q\): "Its coordinates are both zero", the biconditional statement \(p\Leftrightarrow q\) is true.

Answer:

True