Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

I need help with the explanation for how to find if True or False and why...

For the first 3 statements I'm unsure how to check or understand why they are true or false but I believe the the following for them is 50 T, 51 T (If P false and Q false then True... don't understand why P is false in this case though...), 52 T

For Negations, Converse and Contrapositives how do I know if they are true or not? 

Is it if Original in True then Negation is False? If Original True Contrapositive True? What about Converse?

**Question 50**: For all natural numbers \( a \), \( a^2 \equiv 0 \pmod{4} \) or \( a^2 \equiv 1 \pmod{4} \). **Question 51**: For all natural numbers \( a \), if \( a^2 \equiv 2 \pmod{4} \), then \( 1 = 2 \). **Question 52**: For all natural numbers \( a \), if \( a^2 \equiv 2 \pmod{4} \), then \( 1 \neq 2 \). **Question 53**: The negation of #51 is true. **Question 54**: The negation of #52 is true. **Question 55**: The converse of #51 is true. **Question 56**: The converse of #52 is true. **Question 57**: The contrapositive of #51 is true. **Question 58**: The contrapositive of #52 is true. **Question 59**: The contrapositive of #52 is true.
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Transcribed Image Text:**Question 50**: For all natural numbers \( a \), \( a^2 \equiv 0 \pmod{4} \) or \( a^2 \equiv 1 \pmod{4} \). **Question 51**: For all natural numbers \( a \), if \( a^2 \equiv 2 \pmod{4} \), then \( 1 = 2 \). **Question 52**: For all natural numbers \( a \), if \( a^2 \equiv 2 \pmod{4} \), then \( 1 \neq 2 \). **Question 53**: The negation of #51 is true. **Question 54**: The negation of #52 is true. **Question 55**: The converse of #51 is true. **Question 56**: The converse of #52 is true. **Question 57**: The contrapositive of #51 is true. **Question 58**: The contrapositive of #52 is true. **Question 59**: The contrapositive of #52 is true.
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