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Review Sheet Chapter Two. Symbols : Venn Diagrams : Overlaps: Some shared portion (both true) No overlap: nothing in common Completely inside: all of the smaller are part of the bigger; but not the other way around Logic Laws:
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Review Sheet Chapter Two Symbols: Venn Diagrams: Overlaps: Some shared portion (both true) No overlap: nothing in common Completely inside: all of the smaller are part of the bigger; but not the other way around Logic Laws: Law of syllogism: pq, qr, so pr example: If it snows, we miss school. If we miss school, you sleep in. If it snows, you sleep in. Law of detachment: pq is true statement; so if p is true, then q must be example: If you have 4 tardies, you get ISS. Tym has 4 tardies. Tym will get ISS Statements: Test Taking Tips: Stop and think – don’t hurry through; Does the sentence make any sense C B and C share and so do C and D B and D don’t All A’s are B’s, but not all B’s are A’s B A D
Pictures and games, but also internet Pictures, but no games
Triangles and Logic • SSM: • no help Contrapositive is a flip and a negate flip changes order of statements and negate adds a not to both (remember a double negative is a positive!)
if and only if is a biconditional statement represented by • or is represented by • Therefore is represented by • and is represented by Let m represent: Angle A is obtuse. Let n represent: Angle B is obtuse. Which is a symbolic representation of the following argument? Angle A is obtuse if and only if Angle B is obtuse. Angle A is obtuse or Angle B is obtuse. Therefore, Angle A is obtuse and Angle B is obtuse. A. m → n B. m → n C. m ↔ n D. m ↔ n m ∧ n m ∨ n m ∧ n m ∨ n ∴ m ∨ n ∴ m ∧ n ∴ m ∨ n ∴ m ∧ n m n Angle A is obtuse if and only if Angle B is obtuse. Angle A is obtuse or Angle B is obtuse. Therefore, Angle A is obtuse and Angle B is obtuse. m n m n
if and only if is a biconditional statement represented by • or is represented by • Therefore is represented by • and is represented by pq pq pq
Triangles and Logic • SSM: • Check to see which answers make sense when you read them • D does not fit the pattern Just because some snakes live in the water does not mean that they are fish
Ch 2 Coordinate Relations and Transformations • SSM: • test each area * Flute and oboe is the intersections of the Flute and Oboe circles. Overlaps with other circles must be eliminated because of the word “only”
Ch 2 Coordinate Relations and Transformations • SSM: • look for conclusion that has the parts of the statements • draw figures to illustrate answers Rhombus is parallelogram and parallelogram has opposite angles congruent; so combine rhombus has opposite angles congruent
Ch 2 Coordinate Relations and Transformations • SSM: • inverse negate Remember the order: converse flip inverse negate contrapositive both Negate the hypotheses and the conclusion.
Ch 2 Reasoning, Lines, and Transformations Some are both All I are E All E are I None are both Equilateral triangles have 3 sides equal and isosceles triangle have 2 sides equal • SSM: • draw triangles
Ch 2 Reasoning, Lines, and Transformations • SSM: • think of it as a puzzle ~p p ~q q Brent works this summer is in first line normally and in the third line with a not. Brent takes a vacation appears in the second line If .., then … . not ~ therefore
Ch 2 Reasoning, Lines, and Transformations • SSM: • draw a rhombus • eliminate statements that are false Given mentions parallelograms, opposite angles and rhombus. Plug rhombus in for parallelogram in if then statement. (Look for any answer that has two of these terms)
Ch 2 Reasoning, Lines, and Transformations • SSM: • remember order:converse Flipinverse Negatecontrapositive Both Converse says to flip the conclusion and the hypotenuse order.
