Let T (c, d) mean “c is taller than d,” G(c) mean “c is a giraffe,” N (c) mean “c is a gnu,” L(c) mean “c is a lion, and Z(c) mean “c is a zebra. Then from the axioms (I) (∀c)(∀d)(G(c) →(N (d) →T (c, d))) (every giraffe is taller than every gnu), (II) (∃c)(N (c)∧(∀d)(L(d) →T (c, d))) (some gnu is taller than every lion), and (III) (∃c, d)(L(c) ∧Z(d) ∧T (c, d)) (some lion is taller than some zebra),1 prove that every giraffe is taller than some zebra, i.e., (∀c)(G(c) →(∃d)(Z(d) ∧T (c, d))).
Let T (c, d) mean “c is taller than d,” G(c) mean “c is a giraffe,” N (c) mean “c is a gnu,” L(c) mean “c is a lion, and Z(c) mean “c is a zebra. Then from the axioms (I) (∀c)(∀d)(G(c) →(N (d) →T (c, d))) (every giraffe is taller than every gnu), (II) (∃c)(N (c)∧(∀d)(L(d) →T (c, d))) (some gnu is taller than every lion), and (III) (∃c, d)(L(c) ∧Z(d) ∧T (c, d)) (some lion is taller than some zebra),1 prove that every giraffe is taller than some zebra, i.e., (∀c)(G(c) →(∃d)(Z(d) ∧T (c, d))).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Let T (c, d) mean “c is taller than d,” G(c) mean “c is a giraffe,” N (c)
mean “c is a gnu,” L(c) mean “c is a lion, and Z(c) mean “c is a zebra.
Then from the axioms
(I) (∀c)(∀d)(G(c) →(N (d) →T (c, d))) (every giraffe is taller than every
gnu),
(II) (∃c)(N (c)∧(∀d)(L(d) →T (c, d))) (some gnu is taller than every lion),
and
(III) (∃c, d)(L(c) ∧Z(d) ∧T (c, d)) (some lion is taller than some zebra),1
prove that every giraffe is taller than some zebra, i.e.,
(∀c)(G(c) →(∃d)(Z(d) ∧T (c, d))).
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