Additional exercises K EXERCISE 1.9.1: Proof by contrapositive of statements about odd and even integers. Prove each statement by contrapositive (a) For every integer n, if n² is odd, then n is odd. (b) For every integer n, if n° is even, then n is even. (c) For every integer n, if 5n + 3 is even, then n is odd. (d) For every integer n, if n² – 2n +7 is even, then n is odd. (e) For every integer n, if n2 is not divisible by 4, then n is odd. (f) For every pair of integers x and y, if xy is even, then x is even or y is even. (g) For every pair of integers and y, if x – y is odd, then x is odd or y is odd. (h) If n is an integer such that n2 3 and 2n-1 is prime, then n is odd. Feedback?
Additional exercises K EXERCISE 1.9.1: Proof by contrapositive of statements about odd and even integers. Prove each statement by contrapositive (a) For every integer n, if n² is odd, then n is odd. (b) For every integer n, if n° is even, then n is even. (c) For every integer n, if 5n + 3 is even, then n is odd. (d) For every integer n, if n² – 2n +7 is even, then n is odd. (e) For every integer n, if n2 is not divisible by 4, then n is odd. (f) For every pair of integers x and y, if xy is even, then x is even or y is even. (g) For every pair of integers and y, if x – y is odd, then x is odd or y is odd. (h) If n is an integer such that n2 3 and 2n-1 is prime, then n is odd. Feedback?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:|1.7.3: Valid and invalid arguments in English.
EXERCISE
Which of the following arguments are invalid and which are valid? Prove your answer by replacing each proposition with a variable to
obtain the form of the argument. Then prove that the form is valid or invalid.
(a)
The patient has high blood pressure or diabetes or both.
The patient has diabetes or high cholesterol or both.
: The patient has high blood pressure or high cholesterol.
(b)
He studied for the test or he failed the test or both.
He passed the test.
:: He studied for the test.
(c)
If v2 is an irrational number, then 2/2 is an irrational number.
2/2 is an irrational number.
: V2 is an irrational number.
(d)
4 is an odd integer or 4 is a negative integer.
4 is not a negative integer.
.. 4 is an odd integer.
Transcribed Image Text:Additional exercises
K EXERCISE
1.9.1: Proof by contrapositive of statements about odd and even integers.
Prove each statement by contrapositive
(a) For every integer n, if n² is odd, then n is odd.
(b) For every integer n, if n° is even, then n is even.
(c) For every integer n, if 5n + 3 is even, then n is odd.
(d) For every integer n, if n² – 2n +7 is even, then n is odd.
(e) For every integer n, if n2 is not divisible by 4, then n is odd.
(f) For every pair of integers x and y, if xy is even, then x is even or y is even.
(g) For every pair of integers and y, if x – y is odd, then x is odd or y is odd.
(h) If n is an integer such thatn2 3 and 2n-1 is prime, then n is odd.
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