![]() ![]() Take the first conditional statement from above:Ĭonclusion: … then my homework will be eaten.Ĭonverse: If my homework is eaten, then I have a pet goat. You may "clean up" the two parts for grammar without affecting the logic. To create a converse statement for a given conditional statement, switch the hypothesis and the conclusion. Whether the conditional statement is true or false does not matter (well, it will eventually), so long as the second part (the conclusion) relates to, and is dependent on, the first part (the hypothesis). If the quadrilateral has four congruent sides and angles, then the quadrilateral is a square.Įach of these conditional statements has a hypothesis ("If …") and a conclusion (" …, then …"). If I ask more questions in class, then I will understand the mathematics better. If I eat lunch, then my mood will improve. If the polygon has only four sides, then the polygon is a quadrilateral. If I have a triangle, then my polygon has only three sides. If I have a pet goat, then my homework will be eaten. In logic, concepts can be conditional, using an if-then statement: Then we will see how these logic tools apply to geometry. To understand biconditional statements, we first need to review conditional and converse statements. One example is a biconditional statement. Geometry and logic cross paths many ways. If we remove the if-then part of a true conditional statement, combine the hypothesis and conclusion, and tuck in a phrase "if and only if," we can create biconditional statements. Both the conditional and converse statements must be true to produce a biconditional statement. ![]() A biconditional statement combines a conditional statement with its converse statement. ![]()
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