MAT 300, Spielberg Section 3.2 Homework Fall 2005
3.2.4(2-5). Describe each set in two ways:
(i) {xโA๎
๎P(x)}
(ii) {f(x)๎
๎xโA}.
A. For each of the following statements, state which variables are free and which are bound.
Rewrite each statement in an equivalent form using logical notation (including quantifiers,
if necessary), but without using the set braces โ{โ and โ}.โ In each case, if the statement
has no free variables, decide whether it is true or false, and explain your reasoning.
(A1) The sets {n2๎
๎nโZ}and {n3๎
๎nโZ}have at least one common element.
(A2) The sets {x+n๎
๎nโZ}and {y+n๎
๎nโZ}have no elements in common.
(A3) yโ {xโZ๎
๎3 divides x}.
(A4) 2 โ๎wโZ๎
๎
๎66โ {xโZ๎
๎wdivides x}๎.
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