Unit Study #3 (RSN)
RSN01
In a conditional statement, the hypothesis follows the "if," and the conclusion follows the
"then." For example, "If I am wearing a jacket, then it is cold outside."
RSN02
I can change a statement, into a conditional statement. For example, the statement is,
"When corresponding angles are congruent, they are on parallel lines." To change this
into a conditional, you need to add an if, and then. Therefore, "If corresponding angles
are congruent, then they are on parallel lines."
RSN03
Given a set of conditional statements, I can put them in order of a logic chain.
For example, if I am given the following statements:
If sunny, then hot
If day, then sunny
If beach, then surfing
If hot, then beach
You can put these in order...
1) If day, then sunny
2) If sunny, then hot
3) If hot, then beach
4) If beach, then surfing
RSN04
Given a conditional statement, I can write the converse, inverse, and contrapositive
of the conditional. For example, take this conditional, "If there are waves, then I am
surfing." To make the converse, flip the hypothesis and conclusion, but keep the "if"
and "then" where they are. "If I am surfing, then there are waves." To create the
inverse, take the conditional and add "not" into the hypothesis and conclusion to get,
"If there are not waves, then I am not surfing." For the contrapositive, take the
converse, and add "not" into the hypothesis and conclusion. "If I am not surfing, then
there are not waves."
RSN05
I can use the converse, inverse, and contrapositive to determine the validity of a
conclusion made in association with conditional statements. Given this conditional,
"If you are 15 years old, then you are a teenager," you can create a converse, inverse,
and contrapositive. Is the converse true, "If you are a teenager, then you are 15 years
old." No, because there are other ages of teenagers, 13, 14, 16, 17, 18, and 19. Is this
inverse true, "If you are not 15 years old, then you are not a teenager." No, the counter
for this is the same. There are many other teen-ages. What about the contrapositive,
"If you are not a teenager, then you are not 15 years old." Yes, if you are not a teen
within those ages then you cannot be 15.
RSN06
Given a conditional statement, you can create a biconditional that will work both ways.
Take the following conditional, "If water, then H2O." This biconditional would be written
as, "Water iff H2O." The iff means, "if and only if." You would also draw a small line
under the iff to indicate that it works both ways. But sometimes it doesn't always work
both ways, therefore the biconditional doesn't work. It is not valid.
RSN07
To determine if a definition is good or not, but the conditional into a biconditional, and
examine it to determine if the biconditional is valid. If the biconditional is valid, then
it is a good definition.
RSN08
Given a statement, determining the opposite, is called logical negation. By determining
everything opposite of the statement, you can prove the statement true, by narrowing
down everything opposite of the statement is not valid. Therefore, the statement must
be true.
RSN09
I can use Euler Diagrams to demonstrate whether a statement is a contradiction or not. From this diagram,
You can see all the different types of quadrilaterals,
including the three major categories, parallelograms,
trapezoids, and kites. You can identify that while, a
trapezoid is always a quadrilateral, but is never a parallelogram because a parallelogram has two pairs of parallels sides, while trapezoids
have only one. If a shape is in the kite category, can it also be in the trapezoid or
parallelogram? No, because or else, the kite circle would be in one of those. A mark outside
of the quadrilateral diagram would mean that it is not a quadrilateral, therefore cannot be
anything inside of the diagram.
RSN01
In a conditional statement, the hypothesis follows the "if," and the conclusion follows the
"then." For example, "If I am wearing a jacket, then it is cold outside."
RSN02
I can change a statement, into a conditional statement. For example, the statement is,
"When corresponding angles are congruent, they are on parallel lines." To change this
into a conditional, you need to add an if, and then. Therefore, "If corresponding angles
are congruent, then they are on parallel lines."
RSN03
Given a set of conditional statements, I can put them in order of a logic chain.
For example, if I am given the following statements:
If sunny, then hot
If day, then sunny
If beach, then surfing
If hot, then beach
You can put these in order...
1) If day, then sunny
2) If sunny, then hot
3) If hot, then beach
4) If beach, then surfing
RSN04
Given a conditional statement, I can write the converse, inverse, and contrapositive
of the conditional. For example, take this conditional, "If there are waves, then I am
surfing." To make the converse, flip the hypothesis and conclusion, but keep the "if"
and "then" where they are. "If I am surfing, then there are waves." To create the
inverse, take the conditional and add "not" into the hypothesis and conclusion to get,
"If there are not waves, then I am not surfing." For the contrapositive, take the
converse, and add "not" into the hypothesis and conclusion. "If I am not surfing, then
there are not waves."
RSN05
I can use the converse, inverse, and contrapositive to determine the validity of a
conclusion made in association with conditional statements. Given this conditional,
"If you are 15 years old, then you are a teenager," you can create a converse, inverse,
and contrapositive. Is the converse true, "If you are a teenager, then you are 15 years
old." No, because there are other ages of teenagers, 13, 14, 16, 17, 18, and 19. Is this
inverse true, "If you are not 15 years old, then you are not a teenager." No, the counter
for this is the same. There are many other teen-ages. What about the contrapositive,
"If you are not a teenager, then you are not 15 years old." Yes, if you are not a teen
within those ages then you cannot be 15.
RSN06
Given a conditional statement, you can create a biconditional that will work both ways.
Take the following conditional, "If water, then H2O." This biconditional would be written
as, "Water iff H2O." The iff means, "if and only if." You would also draw a small line
under the iff to indicate that it works both ways. But sometimes it doesn't always work
both ways, therefore the biconditional doesn't work. It is not valid.
RSN07
To determine if a definition is good or not, but the conditional into a biconditional, and
examine it to determine if the biconditional is valid. If the biconditional is valid, then
it is a good definition.
RSN08
Given a statement, determining the opposite, is called logical negation. By determining
everything opposite of the statement, you can prove the statement true, by narrowing
down everything opposite of the statement is not valid. Therefore, the statement must
be true.
RSN09
I can use Euler Diagrams to demonstrate whether a statement is a contradiction or not. From this diagram,
You can see all the different types of quadrilaterals,
including the three major categories, parallelograms,
trapezoids, and kites. You can identify that while, a
trapezoid is always a quadrilateral, but is never a parallelogram because a parallelogram has two pairs of parallels sides, while trapezoids
have only one. If a shape is in the kite category, can it also be in the trapezoid or
parallelogram? No, because or else, the kite circle would be in one of those. A mark outside
of the quadrilateral diagram would mean that it is not a quadrilateral, therefore cannot be
anything inside of the diagram.
RSN10
Given a set of conditions and related statements, I can apply indirect reasoning to come to
conclusion. For example, If it is raining outside, then my umbrella will be wet. My umbrella is
dry. What can you conclude using indirect reasoning? -It is not raining outside. This is from
the contrapositive. Another example, If the dog ate my homework then he looks guilty. The dog looks guilty. Can you apply indirect reasoning to conclude that the dog ate my homework? -No, there could be other reasons. You cannot apply this from the converse.
Given a set of conditions and related statements, I can apply indirect reasoning to come to
conclusion. For example, If it is raining outside, then my umbrella will be wet. My umbrella is
dry. What can you conclude using indirect reasoning? -It is not raining outside. This is from
the contrapositive. Another example, If the dog ate my homework then he looks guilty. The dog looks guilty. Can you apply indirect reasoning to conclude that the dog ate my homework? -No, there could be other reasons. You cannot apply this from the converse.
RSN12
I can use a two column proof to solve an algebraic equation. First, set up a T-chart. Label
the left side as statements and the right side as reasons. Place your given statement at the
top of the left column, and the statement you are proving at the bottom of that column. Each
time you add, subtract, divide, or multiply, you write out the statement you will get as a result
of this action and state addition property of equality (or x, -, etc.), on the reasons side. Each
action you do, you need to specifically justify that action with why you are able to do so. On the left, is an example of a simple
algebraic proof.
I can use a two column proof to solve an algebraic equation. First, set up a T-chart. Label
the left side as statements and the right side as reasons. Place your given statement at the
top of the left column, and the statement you are proving at the bottom of that column. Each
time you add, subtract, divide, or multiply, you write out the statement you will get as a result
of this action and state addition property of equality (or x, -, etc.), on the reasons side. Each
action you do, you need to specifically justify that action with why you are able to do so. On the left, is an example of a simple
algebraic proof.
RSN13
I can complete a proof of overlapping angles theorem and overlapping segments theorem.
I can complete a proof of overlapping angles theorem and overlapping segments theorem.