![]() Remember, a conditional and its contrapositive are either both true If and only if each element of C is in A, in B, To prove a biconditional, one proves the two corresponding conditionals.Īn example of the definition of union written as a Proof, we will try to find a counterexample and prove it false.Īn "if and only if" (often abbreviated iff) statement is called aīiconditional and combines the statements p=> q Where p is true, sometimes, instead of writing a long Since to be true, a conditional must be true for every situation Please review especially the symbols for conditional, converse, inverse,Īnd terms statement, conjecture, biconditional,Īntecedent (hypothesis), consequent (conclusion)Ī counterexample of a conditional p=> q is What we prove are often logical statements in the form if-thenĪnd we must follow the rules of logic to form these proofs. Some geometries state each definition in the form of a biconditional. In Geometry we must define things and often generate proofs. Please review especially the terms union, intersection, element, subset, null or empty set Their elements will often be referred to collectively and symbolically. Thus the sets will often be of infinite extent and thus In Geometry, we will primarily be forming the unions and intersections Definitions and Polygons Back to the Table of Contents A Review of Basic Geometry - Lesson 2 Good Definitions as Biconditionals Polygons Lesson Overview ![]()
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