1. If any of the following arguments is valid, provide a proof outline (see example). [Your proof outline should insert two sentences as steps in between the premises and conclusion, as shown in the example below. Also write down the line numbers of the earlier statements used - a maximum of two - next to each step.] If it isn't valid then draw a counterexample world. argument a = b Example: BackOf(b, c) SameRow(c, d) Proof outline 1. a = b 2. BackOf(b, c) 3. SameRow(c, d) FrontOf(d, a) 4. BackOf(a, c) 5. BackOf(a, d) (1, 2) (3,4) 6. FrontOf(d, a) (5) (i) Adjoins(a, b) (11) SameRow(c, b) Tet(b) v Cube(c) Tet(a) (iii) SameSize(b, c) LeftOf(a, c) SameShape(a, b) Tet(c) A Tet(b) SameRow(b, c) SameRow(a, c) ― Dodec(c) b = c 2. Show that the following argument is valid by providing a formal proof. (Fill in the lines 4, 5 and 6, citing rules of inference, and fill in the rule for line 7.) 1 RightOf(a, c) 2 a=b d = c 234567 7| RightOf(b, d)

1. If any of the following arguments is valid, provide a proof outline (see example). [Your proof outline should insert two sentences as steps in between the premises and conclusion, as shown in the example below. Also write down the line numbers of the earlier statements used - a maximum of two - next to each step.] If it isn't valid then draw a counterexample world. argument a = b Example: BackOf(b, c) SameRow(c, d) Proof outline 1. a = b 2. BackOf(b, c) 3. SameRow(c, d) FrontOf(d, a) 4. BackOf(a, c) 5. BackOf(a, d) (1, 2) (3,4) 6. FrontOf(d, a) (5) (i) Adjoins(a, b) (11) SameRow(c, b) Tet(b) v Cube(c) Tet(a) (iii) SameSize(b, c) LeftOf(a, c) SameShape(a, b) Tet(c) A Tet(b) SameRow(b, c) SameRow(a, c) ― Dodec(c) b = c 2. Show that the following argument is valid by providing a formal proof. (Fill in the lines 4, 5 and 6, citing rules of inference, and fill in the rule for line 7.) 1 RightOf(a, c) 2 a=b d = c 234567 7| RightOf(b, d)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...

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