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# Logic Practice Set 1 (page 2)

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Updated on Aug 10, 2011

1. a. Since one-half of the four children are girls, two must be boys. It is not clear which children have blue or brown eyes.
2. d. All baseball caps have brims, since baseball caps are hats (Fact 3) and all hats have brims (Fact 1). This rules out statement III—but it doesn't follow that all caps, a category that may include caps that are not baseball caps, have brims (statement I). Statement II cannot be confirmed, either, since it is possible, given the information, that all baseball caps are black.
3. b. The first statement cannot be true because only female birds lay eggs. Statement II is true because hens are chickens and chickens are birds. Statement III is also true because if only some chickens are hens, then some must not be hens.
4. d. None of the three statements is supported by the known facts.
5. c. Statements I and II are not supported by the facts. Statement III is true because if all storybooks have pictures and only some have words, then some storybooks have both words and pictures.
6. d. There is not enough information to support any of the statements. Robert is known to have a minvan, but it is not known which of his vehicles is red. Robert may have a pickup or sport utility vehicle, so the second statement cannot be supported. There is no way to know if Robert's favorite color is red (statement III).
7. a. Since Maui is an island and islands are surrounded by water, Maui must be surrounded by water. There is not enough information to support statements II and III.
8. c. If all drink mixes are beverages and some beverages are red, then some drink mixes are red (statement I). Since all beverages are drinkable and all drink mixes are beverages, then all red drink mixes must be drinkable (statement III). Statement II can be ruled out.
9. d. There is no information in the facts to support statements I or II. Statement III is clearly wrong because, according to Fact 1, no frames cost less than \$35.
10. b. Since some pens don't write, some writing utensils don't write (statement I). Since there are blue pens and since pens are writing utensils, some writing utensils are blue (statement II). There is not enough information to support statement III.
11. c. If Mary always tells the truth, then both Ann and Mary have cats (statements I and II), and Ann is lying (statement III).
12. b. Statement II is the only true statement. Since all dogs like to run, then the ones who like to swim also like to run. There is no support for statement I or statement III.

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