G.1 The student will construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include a) identifying the converse, inverse, and contrapositive of a conditional statement; b) translating a short verbal argument into symbolic form; c) using Venn diagrams to represent set relationships; and d) deductive reasoning. G.1a Which of the following symbolic forms is the contrapositive of, a b? A. a b B. b a C. b a D. b a G.1a If two angles are supplementary, then the sum of their measures is 180, is a conditional, then if two angles are not supplementary, then the sum of their measures is not 180 is the A. converse B. inverse C. contrapositive D. biconditional G.1a State the converse of the following conditional: If the calculator is not working, then the batteries must be dead. G.1b p: is a right triangle q: is an obtuse triangle ΔABC ΔRST Select one of the following to represent the symbolic representation for each argument. p q q p p q p q p q p q p q is a right triangle, if and only if is an obtuse triangle. ΔABC ΔRST Therefore is a right triangle or is an obtuse triangle. ΔABC ΔRST If is an obtuse triangle, then is a right triangle. ΔRST ΔABC is a right triangle and is an obtuse triangle. ΔABC ΔRST
G.1 The student will construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include a) identifying the converse, inverse, and contrapositive of a conditional statement; b) translating a short verbal argument into symbolic form; c) using Venn diagrams to represent set relationships; and d) deductive reasoning. G.1a Which of the following symbolic forms is the contrapositive of, a b? A. a b B. b a C. b a D. b a G.1a If two angles are supplementary, then the sum of their measures is 180, is a conditional, then if two angles are not supplementary, then the sum of their measures is not 180 is the A. converse B. inverse C. contrapositive D. biconditional G.1a State the converse of the following conditional: If the calculator is not working, then the batteries must be dead. G.1b p: ΔABC is a right triangle q: ΔRST is an obtuse triangle Select one of the following to represent the symbolic representation for each argument. p q q p p q p q p q p q p q ΔABC is a right triangle, if and only if ΔRST is an obtuse triangle. Therefore ΔABC is a right triangle or ΔRST is an obtuse triangle. If ΔRST is an obtuse triangle, then ΔABC is a right triangle. ΔABC is a right triangle and ΔRST is an obtuse triangle.
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