Inductive Reasoning
Determine whether the conjecture is true.
All colors have an E in them.
What is: False
Explanation: Brown, Black, etc.
What is the converse of this statement?
If you make an insurance claim, then your rates will go up.
What is: If your insurance rates go up, you have made an insurance claim.
Explanation: The hypothesis and conclusion were flipped.
What is the relationship of this statement.
Some people who like dogs also cats.
What is: p∧q
Explanation: The statement uses and/also so we know to use the ∧ symbol.
Use the Law of Detachment to give a valid conclusion.
If you mow the lawn you will get $10.
You mow the lawn.
What is: you will get $10
Explanation: The hypothesis is true and therefore the conclusion is true.
If a = b, then ac = bc
What is: multiplication property of equality
Explanation: If a and b are equivalent then multiplying them by the same variable will equal the same answer.
What the conjecture?
48, 53, 58, 63, 68
What is: add 5
Explanation: One way you can find it is by starting with 68 and subtracting 5 each time. If you so, you will end up with the pattern.
What is the contrapositive of this statement?
If a person is guitar player, then the person is a musician.
What is: If a person is not a musician, then the person is not a guitar player.
Explanation: The hypothesis and conclusion were negated and flipped.
What is the relationship of this statement.
No obtuse angles are less than 90 degrees.
What is: none
Explanation: There is no relationship between obtuse angles and angles less than 90 degrees.
Use the Law of Detachment to give a valid conclusion.
If a number is natural number then it is also a real number.
3 is a natural number.
What is: 3 is a real number
Explanation: The hypothesis is true and therefore the conclusion is true.
If a = b the a may be replaced by b in any expression or equation.
What is: substitution property
Explanation: You can replace a with b because they are equal and won't change the expression/equation.
What is that conjecture?
74, 60, 46, 32, 18
What is: subtract 14
Explanation: One way you can find it is by starting with 18 and adding 14 each time. If you so, you will end up with the pattern.
Determine the truth value by writing the inverse, converse, and contrapositive of this statement.
If rectangle is a square, then a square is a rectangle.
What is: F, F, F
Explanation:
Inverse - If a rectangle is not a square, then a square is not a rectangle. F
Converse - If a square is a rectangle, then a rectangle is a square. F
Contrapositive - If a square is not a rectangle, then a rectangle is not a square. F
What region is this statement referring to?
~p∧q
What is: left
Explanation: The statement is only referring to q so that is the only region that would be shaded.
Use the Law of Syllogism to give a valid conclusion.
If it is Tuesday then you have to take the bus. If you have to take the bus then you don't have to pack your lunch.
What is: if it is tuesday then you don't have to pack your lunch.
Explanation: The conclusion of the first statement is the hypothesis of the second statement.
If AB ≅ CD, then CD ≅ AB
What is: symmetric property of congruence
Explanation: The statement is symmetrical because both terms(?) are equal.
Find the next 4 terms: 1, 4, 9, 25, 36, _, _, _, _
What is: 49, 64, 81, 100
Explanation: Each element is the square of the natural numbers.
Determine the truth value by writing the inverse, converse, and contrapositive of this statement.
If a number is an integer, then it is rational.
What is: T, T, T
Explanation:
Inverse - If a number is not an integer, then it is not rational. F
Converse - If a number is rational, then it is an integer. F
Contrapositive - If a number is not rational, then it is not an integer. T
A school survey found that 53 people had desktops, 76 had laptops, and 12 had both.
1. How many students have a desktop and a laptop?
2. How many students have a laptop but not a desktop?
What is:
Explanation:
1. This would includes all regions because this includes all elements of the diagram.
2. This would include the right region because this is the only one that involved only laptops.
Use the Law of Syllogism to give a valid conclusion.
If you get sick, then you can not go to school. If you get sick, then you can't go to football practice.
What is: no valid conclusion
Explanation: The second statement does not relate to the first statement.
AB + BC = AC
What is: segment addition postulate
Explanation: All of the points are collinear and b is in the middle.
Find the next 4 terms: 3, 2, 18, 62, _, _, _, _, _
What is: 238, 942, 3758, 15022
Explanation: The pattern is to multiply by 4 and subtract 10
Write the conditional and converse to determine if the biconditional statement is true.
I ride by bike if and only if it is not raining.
What is: True
Explanation:
If I ride my bike, then it is not raining. T
If it is not raining, then I ride by bike. T
A school survey found that 243 people liked chocolate ice cream, 518 liked vanilla, and 376 liked both.
1. How many people liked chocolate?
2. How many people liked chocolate or vanilla?
3. How many people liked vanilla but not chocolate?
What is: 619, 1137, and 518
Explanation:
1. This would include the left and center region because both of them involved chocolate.
2. This would includes all regions because this includes all elements of the diagram.
3. This would include the right region because this is the only one that involved only vanilla.
Determine whether the conclusion follows from the given statement by the Law of Detachment or the Law of Syllogism.
If it rains, then you will wear your jacket. If it rains then you can't ride you bike.
Conclusion: If you can't ride my bike, then you will wear your jacket.
What is: invalid
Explanation: I won't wear my jacket just because I can't ride my bike. Other circumstances can occur making the conclusion illogical.
If ∠A is supplementary to ∠B and ∠C is supplementary to ∠B then ∠A ≅ ∠C
What is: congruent segment theorem
Explanation: A is equal to C because both of them are equal to B