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1. |
Determine if the following conjecture is true or false? Explain. Given: x2 = 4
Conjecture: x = 4 or x = -4 |
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A. |
False; the square root of a positive number is always a positive number. |
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B. |
True; squaring a positive number results in a positive number and squaring a negative number results in 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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2. |
Determine the converse of the following if-then statement.
If the flowers are yellow, then they are daffodils. |
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A. |
If the flowers are daffodils, then they are yellow. |
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B. |
If the flowers are not yellow, then they are not daffodils. |
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C. |
The flowers are not daffodils. |
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D. |
The flowers are not yellow. |
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Hint |
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3. |
Write the inverse of the conditional ''If Deanna eats the last cookie, then Leon will buy more.'' |
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A. |
If Leon does not buy more, then Deanna did not eat the last cookie. |
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B. |
If Deanna does not eat the last cookie, then Leon will not buy more. |
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C. |
If Deanna eats the last cookie, then Leon will not buy more. |
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D. |
If Deanna does not eat the last cookie, then Leon will buy more. |
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Hint |
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4. |
What is a valid conclusion to the following hypothesis?
If there are two points... |
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A. |
There are an infinite number of lines containing both points. |
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B. |
There are no lines containing both points. |
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C. |
There is one line containing both points. |
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D. |
There are two lines containing both points. |
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Hint |
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5. |
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 has four right angles. |
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C. |
If WXYZ is not a square, then it does not have four right angles. |
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D. |
If WXYZ has four right angles, then it is a square. |
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Hint |
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6. |
''If you double any number, the result will be an even number.'' is a true conditional. Use the Law of Detachment to reach a logical conclusion. |
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A. |
The result of doubling 234 is an odd number. |
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B. |
The result of doubling 317 is an even number. |
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C. |
When you triple a number, the result must be an even number. |
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D. |
If you double an odd number, the result is another odd number. |
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Hint |
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7. |
Two angles are congruent if they are ______. |
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A. |
vertical |
B. |
supplementary |
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C. |
a linear pair |
D. |
adjacent |
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Hint |
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8. |
In the picture,  and  are vertical. If  then what is  |
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A. |
90 |
B. |
81 |
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C. |
28 |
D. |
162 |
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Hint |
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9. |
A counterexample disproves a conditional when ________ . |
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A. |
the hypothesis is false and the conclusion is false |
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B. |
the hypothesis is true 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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10. |
Which answer shows all the possible subsets of {2,4,5}? |
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A. |
{2}, {4}, {5}, {2,4}, {2,5}, {4,5}, |
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B. |
{2,4,5},{2}, {4}, {5}, {2,4}, {2,5}, {4,5} |
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C. |
{2,4,5},{2}, {4}, {5}, {2,4}, {2,5}, {4,5}, |
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D. |
{2,4,5},{2}, {4}, {5}, |
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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 A= {0,1,2,3,4}, B={2,4,6,8} and C= {-3, -2, -1, 0}, find |
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A. |
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B. |
{-3, -2, -1, 0, 2, 4, 6, 8} |
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C. |
{2,4,6,8} |
D. |
{-3, -2, -1, 0} |
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Hint |
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13. |
If and  Which shows  |
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A. |
{2, 4, 6, 8, 10} |
B. |
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C. |
{1, 2, 3, 4, 5, 6} |
D. |
{1, 2, 3, 4, 5, 6, 8, 10 |
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Hint |
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14. |
What is the contrapositive of the conditional If it is September, then there are 30 days in the month? |
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A. |
If it is not 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 September then there are not 30 days in the month. |
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Hint |
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