hw1sol

hw1sol - MATH 55 Prof Bernoff Fall 2007 Harvey Mudd College...

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Unformatted text preview: MATH 55 Prof. Bernoff Fall 2007 Harvey Mudd College Homework 1 – Solutions 1.1 Simplify the following algebraic expression: ( x- a )( x- b )( x- c )( x- z ) . Solution Hint: Consider the twenty-fourth factor. 9.1 Write out the following sets by listing their elements between curly braces. (a) { x ∈ N : x ≤ 10 and 3 | x } . Solution: These are the non-negative multiples of 3 that are also less than 10: { , 3 , 6 , 9 } . (b) { x ∈ Z : x is prime, and 2 | x } . Solution: The prime multiples of 2 are somewhat sparse: { 2 } . (c) { x ∈ Z : x 2 = 4 } . Solution: The solutions to the equation x 2 = 4 are ± 2: {- 2 , 2 } . (d) { x ∈ Z : x 2 = 5 } . Solution: There are no integers that square to 5: ∅ . (e) 2 ∅ . Solution: The only subset of the empty set is the empty set itself: {∅} – notice that this is not the same as the empty set ∅ . (f) { x ∈ Z : 10 | x and x | 100 } ....
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hw1sol - MATH 55 Prof Bernoff Fall 2007 Harvey Mudd College...

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