4. Consider the following statement: For all n N and x € Z, x² = 1 mod n Which of "if", "only if", "iff" in Which of "if", "only if", "iff" in Justify your answers. x = 1 mod n or x = -1 mod n. make this a true statement? make this a false statement?

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 49E: Show that if the statement is assumed to be true for , then it can be proved to be true for . Is...
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4. Consider the following statement:
For all n N and x € Z, x² = 1 mod n
Which of "if", "only if", "iff" in
Which of "if", "only if", "iff" in
Justify your answers.
x = 1 mod n or x = -1 mod n.
make this a true statement?
make this a false statement?
Transcribed Image Text:4. Consider the following statement: For all n N and x € Z, x² = 1 mod n Which of "if", "only if", "iff" in Which of "if", "only if", "iff" in Justify your answers. x = 1 mod n or x = -1 mod n. make this a true statement? make this a false statement?
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I want to know that the situations of "if" in the question.

4. Consider the following statement:
For all n N and x € Z, x² = 1 mod n
Which of "if",
"only if", "iff" in
Which of "if", "only if", "iff" in
Justify your answers.
x = 1 mod n or x = -1 mod n.
make this a true statement?
make this a false statement?
Transcribed Image Text:4. Consider the following statement: For all n N and x € Z, x² = 1 mod n Which of "if", "only if", "iff" in Which of "if", "only if", "iff" in Justify your answers. x = 1 mod n or x = -1 mod n. make this a true statement? make this a false statement?
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