SOL 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) using deductive reasoning, including the law of syllogism. Hints and Notes PRACTICE G.1 Which is the converse of the sentence, Sam leaves, “If Conditional: then I will stay.”? If p, then q. A If I stay, then Sam will p q → B If Sam does not then I will not stay C If Sam leaves then I will not stay. Inverse: Insert “nots” D If I do not stay, then Sam will not If not p, then not q. According to the Venn Diagram, is true? ~p ~q → Converse: Change If q, then p. q→ p Contrapositive: Change order and insert “nots” ~q ~p → A Some football players play offense and defense B All football players play defense Symbols: C No football players play offense and defense ~ not All football players play offense or defense D and or Let a represent is an even number.” if then, implies “x → Let b represent is a multiple of 4.” if and only if “x ↔ When , of the following is true? therefore A Biconditional: B p if and only if q. C p↔q D Law of Syllogism: Which statement is the inverse of the waves are If a→b and b→c, then a→c. “If small, I do not go surfing”? Law of Detachment: A If the waves are not small, I do not go surfing. If a→b is true. B If I do not go surfing, the are small. a is true. C If I go surfing, the waves are not small. b is true. D If the waves are not small, I go surfing.
SOL 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) using deductive reasoning, including the law of syllogism. Hints and Notes Conditional: If p, then q. p → q Inverse: Insert “nots” If not p, then not q. ~p → ~q Converse: Change If q, then p. q→ p Contrapositive: Change order and insert “nots” ~q → ~p Symbols: ~ not and or → if then, implies ↔ if and only if therefore Biconditional: p if and only if q. p↔q Law of Syllogism: If a→b and b→c, then a→c. Law of Detachment: If a→b is true. a is true. b is true. PRACTICE G.1 Which is the converse of the sentence, “If Sam leaves, then I will stay.”? A If I stay, then Sam will B If Sam does not then I will not stay C If Sam leaves then I will not stay. D If I do not stay, then Sam will not According to the Venn Diagram, is true? A Some football players play offense and defense B All football players play defense C No football players play offense and defense D All football players play offense or defense Let a represent “x is an even number.” Let b represent “x is a multiple of 4.” When , of the following is true? A B C D Which statement is the inverse of “If the waves are small, I do not go surfing”? A If the waves are not small, I do not go surfing. B If I do not go surfing, the are small. C If I go surfing, the waves are not small. D If the waves are not small, I go surfing.
York_GeometrySOLReview_2012-13.docx