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Deductive reasoning involves drawing logical conclusions from premises.
Example 1
Mary is faster than John. Dwight is faster than Mary. John is faster than Dwight.
If the first two statements are true, the third statement is: (a)True, (b)False, (c)Uncertain
Solution: (b) Because the first two statements are true, John is the slowest of the three, so the third statement must be false.
Example 2
Julia types slower than Serena. Julia types faster than Cameron. Of all three, Cameron types the slowest.
If the first two statements are true, the third statement is: (a)True, (b)False, (c)Uncertain
Solution: (a) According to the first two statements, Serena types fastest and Cameron types slowest.
1. Broomfield park is south of Arena arcade. Rebecca’s house is northeast of Arena arcade. Rebecca’s house is west of Broomfield park.
If the first two statements are true, the third statement is
(a)True, (b)False, (c)Uncertain
(b) Because the first two statements are true,Rebecca’s house is also northeast of Broomfield park, which means that the thirdstatement is false.
2. A bicycle is practical. Practical things are convenient. A bicycle is convenient.
If the first two statements are true, the third statement is
(a)True, (b)False, (c)Uncertain
(a) To the extent that a bicycle is practical, it is convenient.
3. Fact 1: Mark has four hobbies. Fact 2: Two of the hobbies are kite sports and two of the hobbies are mountain sports. Fact 3: Half of the hobbies are extreme sports.
If the first three statements are facts, which of the following statements must also be a fact?
I. At least one extreme sport is a kite sport. II. Two of the hobbies are not extreme sports. III. None of the mountain sports are extreme sports
(a)II only, (b)I and III only, (c)II and III only, (d)None of the statements is a known fact.
(a) Since one-half of the four hobbies are extreme sports, two of the hobbies are not extreme sports. It is not clear which hobbies are kite sports or mountain sports.
4. Fact 1: Joanna said, “Mark and I both speak French.” Fact 2: Mark said, “I don’t speak French.” Fact 3: Joanna always tells the truth, but Mark sometimes lies.
If the first three statements are facts, which ofthe following statements must also be a fact?
I. Mark speaks French. II. Joanna speaks French. III. Mark is lying.
(a)II only, (b)I and II only, (c)I, II, and III, (d)None of the statements is a known fact.
(c) If Joanna always tells the truth, then both Mark and Joanna speak French (statements I and II), and Mark is lying (statement III).
5. Fact 1: All parrots like to chatter. Fact 2: Some parrots like to sing. Fact 3: Some parrots have red feathers.
If the first three statements are facts, which of the following statements must also be a fact?
I. All parrots who like to sing have red feathers. II. Parrots who like to sing, also like to chatter. III. Parrots who like to chatter do not have red feathers.
(a)I only, (b)II only, (c)II and III only, (d)None of the statements is a known fact.
(b) Statement II is the only true statement. Since all parrots like to chatter, then the ones who like to sing, also like to chatter. There is no support for statement I or statement III.