![]() You can do this if and only if both conditional and converse statements have the same truth value. My polygon has only three sides if and only if I have a triangle.I have a triangle if and only if my polygon has only three sides.Since both statements are true, we can write two biconditional statements: Converse: If my polygon has only three sides, then I have a triangle.Conditional: If I have a triangle, then my polygon has only three sides.If conditional statements are one-way streets, biconditional statements are the two-way streets of logic.īoth the conditional and converse statements must be true to produce a biconditional statement: Notice we can create two biconditional statements. The general form (for goats, geometry or lunch) is:īecause the statement is biconditional (conditional in both directions), we can also write it this way, which is the converse statement: 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. Try this one, too: "If the quadrilateral has four congruent sides and angles, then the quadrilateral is a square."Ĭonverse: If the quadrilateral is a square, then the quadrilateral has four congruent sides and angles. Converse Statement Examplesįor, "If the polygon has only four sides, then the polygon is a quadrilateral," write the converse statement.Ĭonverse: If the polygon is a quadrilateral, then the polygon has only four sides. This converse is true remember, though, neither the original conditional statement nor its converse have to be true to be valid, logical statements. ![]() Let's apply the same concept of switching conclusion and hypothesis to one of the conditional geometry statements: Your homework being eaten does not automatically mean you have a goat. This converse statement is not true, as you can conceive of something … or someone … else eating your homework: your dog, your little brother. Converse: If my homework is eaten, then I have a pet goat.Conclusion: … then my homework will be eaten.Take the first conditional statement from above: 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. ![]()
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