Unformatted text preview: Can you extend this procedure to an arbitrary number of variables? 5. ( 3.2, Prob 1 ) ±or what positive integers x is the statement ( x-2) 2 + 1 ≤ 2 true? ±or what integers is it true? ±or what real numbers is it true? If we expand the universe for which we are considering a statement about a variable, does this always increase the size of the statment’s truth set? 6. ( 3.2, Prob 6 ) Using s ( x, y, z ) to be the statement x = yz and t ( x, y ) to be the statement x < y , write a formal statement for the deFnition of the greatest common divisor of two numbers. 7. ( 3.2, Prob 10 ) Rewrite the following statement without any negations: It is not the case that there exists an integer n such that n > 0 and for all integers m > n , for every polynomial equation p ( x ) = 0 of degree m there are no real numbers for solutions. 1...
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- Spring '11
- Logic, Distributivity, PROB, Amitabha Bagchi