Consider statement P: "For all integers n, if n2 is even, then n is even." 1. Write statement P in predicate logic. Use E(x) for "x is even." 2. Write the contrapositive of statement P in predicate logic. Use O(x) for "x is odd." 3. Give a direct proof of the contrapositive of statement P. 4. In problem 1, you should have recorded a formula for P in predicate logic. Find a formula for the negation of P in predicate logic. Use rules of logic to write this statement using the 3 quantifier and the A connective, and translate this negation back into English. 5. Assume that the negation of P is true. Prove that this assumption leads to a contradiction.
Consider statement P: "For all integers n, if n2 is even, then n is even." 1. Write statement P in predicate logic. Use E(x) for "x is even." 2. Write the contrapositive of statement P in predicate logic. Use O(x) for "x is odd." 3. Give a direct proof of the contrapositive of statement P. 4. In problem 1, you should have recorded a formula for P in predicate logic. Find a formula for the negation of P in predicate logic. Use rules of logic to write this statement using the 3 quantifier and the A connective, and translate this negation back into English. 5. Assume that the negation of P is true. Prove that this assumption leads to a contradiction.
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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Transcribed Image Text:Consider statement P: "For all integers n, if n2 is even,
then n is even."
1. Write statement P in predicate logic. Use E(x) for
"x is even."
2. Write the contrapositive of statement P in
predicate logic. Use O(x) for “x is odd."
3. Give a direct proof of the contrapositive of
statement P.
4. In problem 1, you should have recorded a formula
for P in predicate logic. Find a formula for the
negation of P in predicate logic. Use rules of logic
to write this statement using the 3 quantifier and
the A connective, and translate this negation back
into English.
5. Assume that the negation of P is true. Prove that
this assumption leads to a contradiction.
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