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: pq, qr, so pr example: If it snows, we miss school. If we miss school, you sleep in. If it snows, you sleep in. Law of detachment: pq 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 Symbol Λ V ~    Logical And Or Not Therefore If …, then If and only if Meaning Both Either Opposite conclusion conditional biconditional 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 Statement Symbols Hint Example Conditional P  Q Hypothesis, Conclusion If it snows, we get out of school. Converse Q  P Flip If we get out of school, it snows. Inverse ~P  ~Q Negate If it didn’t snow, we don’t get out of school. Contrapositive ~Q  ~P Both If we don’t get out of school, then it didn’t snow.

Pictures and games, but also internet Pictures, but no games

Contrapositive is a flip and a negate 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  pq pq pq

Check to see which answers make sense when you read them 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”

look for conclusion that has the parts of the statements 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

Negate the hypotheses and the conclusion. Ch 2 Coordinate Relations and Transformations SSM: inverse  negate Remember the order: converse flip inverse negate contrapositive both Negate the hypotheses and the conclusion.

Equilateral triangles have 3 sides equal and 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

Brent takes a vacation appears in the second line 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

eliminate statements that are false 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)

remember order: converse Flip inverse Negate contrapositive Both Ch 2 Reasoning, Lines, and Transformations SSM: remember order: converse Flip inverse Negate contrapositive Both Converse says to flip the conclusion and the hypotenuse order.