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GEOMETRY
Logic Worksheet #1: SENTENCES
In 1 – 8, tell whether each is or is not a mathematical sentence.
1) The school day ends at 3:15.
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2) Take the bus.
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3) Are you going?
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4) If John goes.
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5) Atlanta is a city in Alaska.
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6) x + 3 = 2x + 1
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7) Two teaspoons, three times a day.
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8) Do the next seven problems.
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In 9 – 15, all of the sentences are open sentences. Find the variable in each sentence.
9) She is smart.
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10) We elect a president.
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11) It is my favorite color. _______
12) 4y < 20
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13) This is a great country. ________
14) It is a counting number. ________
15) He was the most valuable player in the World Series. ________
In 16 – 23: a) Tell whether the sentence is true, false, or open. b) If the sentence is an
open sentence, identify the variable.
16) The United States of America declared independence in 1776.
17) They celebrate Independence Day on July 14 every year.
18) San Francisco is a city in New York State.
19) A rectangle is a four-sided polygon.
20) 5x + 2 = 17
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21) 5(10) + 2 = 17
22) 5(3) + 2 = 17
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23) 23 = 32
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In 24 – 28, use the replacement set {New York, Florida, California, Hawaii, Kansas} to
find the truth set for each open sentence.
24) It was one of the last two states admitted to the U.S.A.
25) It does not border or touch an ocean.
26) It is on the east coast on the United States.
27) Its capital is Sacramento.
28) It is one of the states of the United States of America.
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In 29 – 36, use the domain of natural numbers to find the solution set for each open
sentence. It is possible that no replacements make true sentences.
29) x + 5 = 17
31) 56 = 3x – 4
33) 2x – x = 1
35) x + 1 < 6
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30) x – 5 = 17
32) 2x + x = 6
34) x < 3
36) .2x + 3 = 6
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