Consider the statement "for all integers a and b, if a + b is even, then a and b are even" (a) Write the contrapositive of the statement. (b) Write the converse of the statement. (c) Write the negation of the statement. (d) Is the original statement true or false? Prove your answer. (e) Is the contrapositive of the original statement true or false? Prove your answer. (f) Is the converse of the original statement true or false? Prove your answer. (g) Is the negation of the original statement true or false? Prove your answer.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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**Exercise: Logical Statements and Their Forms**

Consider the statement "For all integers \(a\) and \(b\), if \(a + b\) is even, then \(a\) and \(b\) are even."

**Tasks:**

(a) Write the contrapositive of the statement.

(b) Write the converse of the statement.

(c) Write the negation of the statement.

(d) Is the original statement true or false? Prove your answer.

(e) Is the contrapositive of the original statement true or false? Prove your answer.

(f) Is the converse of the original statement true or false? Prove your answer.

(g) Is the negation of the original statement true or false? Prove your answer.
Transcribed Image Text:**Exercise: Logical Statements and Their Forms** Consider the statement "For all integers \(a\) and \(b\), if \(a + b\) is even, then \(a\) and \(b\) are even." **Tasks:** (a) Write the contrapositive of the statement. (b) Write the converse of the statement. (c) Write the negation of the statement. (d) Is the original statement true or false? Prove your answer. (e) Is the contrapositive of the original statement true or false? Prove your answer. (f) Is the converse of the original statement true or false? Prove your answer. (g) Is the negation of the original statement true or false? Prove your answer.
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