210hw2 - “necessary condition” and “sufficient condition” 2 Construct a truth table for P ± ¬ Q ∨ P ² Can you find a simpler

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Math 210 Homework 2 Due Wednesday February 23rd 1. (This example is due to Lewis Carroll.) Consider the statements: Animals that do not kick are always unexcitable. Donkeys have no horns. A buffalo can always toss you over a gate. No animals that kick are easy to swallow. No hornless animal can toss you over a gate. All animals are excitable except buffaloes. (i) What’s a reasonable choice for a universe of discourse? (ii) Choose letters to represent the various predicates that appear, and rewrite each statement using symbols. (iii) Choose one of the six statements and rephrase it using the expressions
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Unformatted text preview: “necessary condition” and “sufficient condition”. 2. Construct a truth table for P ∧ ± ( ¬ Q ) ∨ P ² . Can you find a simpler expression that always has the same truth value as P ∧ ± ( ¬ Q ) ∨ P ² ? 3. Show that h ( P → Q ) ∧ ( Q → R ) i → ( P → R ) is a tautology. 4. List the distinct elements in each set. (i) { x ∈ Z ³ ³ ³ xy = 15 for some y ∈ Z } (ii) n x + y ³ ³ ³ x ∈ {-1 , , 1 } , y ∈ { , 1 , 2 } o 5. Classify as true or false. ∅ ⊆ {∅} ∅ ∈ {∅} { 1 , 2 } ∈ n 1 , 2 , { 3 , 4 } o { 3 , 4 } ⊆ n 1 , 2 , { 3 , 4 } o 1...
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This note was uploaded on 12/07/2011 for the course MATH 210 taught by Professor Staff during the Spring '08 term at University of Delaware.

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