M135F07A3

# M135F07A3 - MATH 135 Assignment #3 Hand-In Problems 1....

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MATH 135 Fall 2007 Assignment #3 Due: Wednesday 03 October 2007, 8:20 a.m. Hand-In Problems 1. Throughout this problem, the universe of discourse is R , the real numbers. (a) Is “ x y, x 2 + 1 = y 2 ” TRUE or FALSE? Explain. (b) Is “ x y, x 2 + 1 = y 2 ” TRUE or FALSE? Explain. (c) Is “ x y, x 2 + 1 = y 2 ” TRUE or FALSE? Explain. (d) Is “ x y, x 2 + 1 = y 2 ” TRUE or FALSE? Explain. (e) Is “ y x, x 2 + 1 = y 2 ” TRUE or FALSE? Explain. 2. Express the following English language statements using quantiﬁers. Throughout this problem, the universe of discourse is Z , the integers. (a) “Every integer is 7 more than some integer.” (b) “There is an integer that divides into every integer.” 3. For each pair a and b , state the quotient and remainder when a is divided by b . (a) a = 387, b = 11 (b) a = - 387, b = 11 (c) a = 387, b = - 11 (d) a = - 387, b = - 11 4. (a) Determine gcd(987 , 320). (b) Determine integers

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## M135F07A3 - MATH 135 Assignment #3 Hand-In Problems 1....

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