Assignment - Homework 3

# Assignment - Homework 3 - x are equiva-lent 3 x 2 is...

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Homework 3 MA 2312 Due Tuesday at the beginning of your recitation 1. Prove that if n is a positive integer, n is even if and only if 7 n + 4 is even. 2. Prove that 5 divides n if and only if 5 divides n 2 . 3. Prove or disprove that 2 n - 1 is prime for all integers n . (Primes of the form 2 n - 1 are called Mersenne primes). 4. Show the following two statements about a real number
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Unformatted text preview: x are equiva-lent: 3 x + 2 is irrational. x/ 2 is irrational. 5. Prove that if n is a prefect square, n + 2 is not a perfect square. 6. Prove that if A ⊆ B then 2 A ⊆ 2 B . 7. Prove that A-( B ∩ C ) = ( A-B ) ∪ ( A-C ). 8. Solve for x: 200 X i =2 i 3 = x + 9 X i =3 i 3 + 200 X k =11 k 3 1...
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