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1. |
Looking at several specific situations to arrive at an educated guess is called __________. |
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A. |
a conjecture |
B. |
guessing |
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C. |
inductive reasoning |
D. |
deductive reasoning |
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Hint |
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2. |
Determine if the following conjecture is true or false? Explain. Given: x2 = 4
Conjecture: x = 4 or x = -4 |
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A. |
True; squaring a positive number results in a positive number and squaring a negative number results in a positive number. |
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B. |
False; the square root of a positive number is always a positive number. |
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C. |
False; the square root of 4 is 2 or -2. |
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D. |
True; two answers are always more accurate than one answer. |
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Hint |
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3. |
Determine the contrapositive of the following if-then statement.
If three points are noncollinear, then they form a triangle. |
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A. |
If three points are not noncollinear, then they do not form a triangle. |
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B. |
If three points do not form a triangle, then they are not noncollinear. |
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C. |
If three points form a triangle, then they are noncollinear. |
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D. |
If three points do not form a triangle, then they are noncollinear. |
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Hint |
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4. |
The Law of Detachment and other laws of logic can be used to provide a system for reaching logical conclusions, called _____________. |
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A. |
reasonable doubt |
B. |
deductive reasoning |
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C. |
inductive reasoning |
D. |
detachment reasoning |
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Hint |
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5. |
Which statement explains why  |
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A. |
Angles adjacent to the same angle or to congruent angles are congruent. |
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B. |
All right angles are congruent. |
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C. |
Vertical angles are congruent. |
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D. |
Angles complementary to the same angle or to congruent angles are congruent. |
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Hint |
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6. |
Using the following true conditional and hypothesis, which statement would follow from the Law of Detachment?A square has four right angles. WXYZ is a square. |
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A. |
WXYZ has four right angles. |
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B. |
If WXYZ is not a square, then it does not have four right angles. |
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C. |
If WXYZ has four right angles, then it is a square. |
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D. |
If WXYZ is not a square, then it has four right angles. |
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Hint |
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7. |
Which statement explains why  |
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A. |
If two angles form a linear pair, then they are supplementary. |
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B. |
Angles supplementary to the same angle are congruent. |
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C. |
All right angles are congruent. |
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D. |
If the sum of the measures of two angles is 180, then they are supplementary. |
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Hint |
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8. |
A counterexample disproves a conditional when ________ . |
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A. |
the hypothesis is true and the conclusion is false |
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B. |
the hypothesis is false and the conclusion is false |
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C. |
the hypothesis is true and the conclusion is true |
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D. |
the hypothesis is false and there is no valid conclusion |
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Hint |
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9. |
Which of the following is a counterexample to the statement 8k – 1 = 9r for all k, where k and r are integers? |
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A. |
8 = 9 – 1 |
B. |
(84 – 1) ÷ 9 = 455 |
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C. |
83 – 1 = 511, 511 ÷ 9 = 56.8 |
D. |
8(8k) = 8(9r + 1) |
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Hint |
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10. |
How is  read? |
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A. |
A is an element of B. |
B. |
B is an element of A. |
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C. |
B is a subset of A. |
D. |
A is a subset of B. |
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Hint |
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11. |
Which set notation means that 4 is an element of {3,4,5,6}? |
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A. |
4 {3,4,5,6} |
B. |
4 {3,4,5,6} |
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C. |
4 {3,4,5,6} |
D. |
4 {3,4,5,6} |
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Hint |
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12. |
If and  Which shows  |
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{-2, -1, 0, 1, 3} |
B. |
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C. |
{1,3} |
D. |
{-2, -1, 0, 1, 3, 5} |
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Hint |
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13. |
If A = {12, 13, 14, 16, 18} and B = {1, 2, 3, 4, 5, 6}. Which shows A B? |
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A. |
{12, 13, 14, 16, 18} |
B. |
{1, 2, 3, 4, 5, 6} |
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D. |
{1,2,3,4,5,6,12,13} |
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Hint |
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14. |
What is the inverse of the conditional If it is September, then there are 30 days in the month? |
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A. |
If it is September then there are not 30 days in the month. |
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B. |
If there are not 30 days in the month, then it is not September. |
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C. |
If there are 30 day in the month, then it is September. |
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D. |
If it is not September then there are not 30 days in the month. |
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Hint |
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