Given the following, determine the set A ∩ C′. U=x | x ∈ N and x<9
A=x | x ∈ N and x is odd and x<9
C=x | x ∈ N and x<7

n Japan, mixed nuts are the second most popular table nuts, behind sweet chestnuts;[5] in the United States, they are second only to peanuts.[6]Mixed nuts have also gained in popularity in the Argentinian market, which imported some $1.9 million in 1997, nearly half from the U.S.[7] During the year 2002, U.S. companies sold $783 million of mixed nuts incorporating four or more varieties, mostly in canned form, representing hundreds of millions of pounds.[6]

The individual nuts that make up mixed nuts are harvested from all over the world. As a Dallas Fed publication supporting free trade puts it,

"In the average can of mixed nuts, you might find almonds from Italy, walnuts from China, Brazil nuts from Bolivia, cashews from India, pistachios from Turkey, hazelnuts from Canada—a true international assortment."[8]Label on a jar representing eight countries

This reality provides an incentive for nut salters to favor free trade for nuts, as opposed to nut farmers, who would generally support trade barriers. In fact, one historical argument for United States salters is that importing nuts can encourage domestic production, since mixed nuts provide a "wagon" on which everyone's sales ride. For example, cashews are not produced in North America, and it is necessary to import them because mixed nuts are essential to the sale of pecans, which are grown exclusively in North America.[9]

Composition[edit]Mixed nuts by weight

Because they are relatively inexpensive, peanuts are typically a major ingredient in mixed nuts, although they are viewed as less fancy than other nuts; often "deluxe mixed nuts" are advertised as containing no peanuts. In 2006, a batch of "deluxe" mixed nuts was recalled because peanuts had crept into the mix.[10] The move was not to save face: peanuts are the ingredient of mixed nuts most commonly associated with life-threatening food allergies.

"Less than 50% peanuts"

Less dramatically, some mixed nuts advertise themselves to contain "less than 50% peanuts". For a 60 Minutes segment that originally aired in 1997,[11]Andy Rooney tested such a 12-ounce (340 g) can of Planters brand nuts, pleading boredom on a Saturday. He determined that "there was a tiny fraction less than six ounces of peanuts . . . amazing precision for a nut factory."[12] Later, in 2004, a cockeyed.com How much is inside? episode estimated that the peanut weight percentage in two such 11.5 oz cans was, in fact, a little over 50%.[13]

Besides peanuts, cashews are usually the next least expensive nut, and in deluxe mixes they tend to be the most common ingredient.[14] Hazelnuts and Brazil nuts are also "relatively cheap", while pecans are the most expensive ingredient.[12]

Regulations[edit]United States[edit]

Percent composition by weight is a serious matter in the U.S., where mixed nuts have been regulated by the Food and Drug Administration since 1977. Up to that point, the phrase "mixed nuts" had been legally meaningless. A 1964 Consumer Reports investigation of 124 cans of mixed nuts, representing 31 brands bought in 17 American cities, determined that most mixed nuts of the time were mostly peanuts, often 75%; peanutless brands were usually dominated by cashews. Many cans bore misleading labels or were underfilled. Consumer Reports concluded, "What's needed of course is a Federal standard of identity...", detailing a list that of requirements that, with the exception of their desire to limit broken nuts, anticipated the 1977 rules.[14]

On March 15, 1977, the FDA promulgated a new standard of identity for mixed nuts in 42 FR 14475. The present standard, as modified by 58 FR 2885, Jan. 6, 1993, requires that mixed nuts must contain at least four different varieties of tree nuts or peanuts. (Products with three or fewer varieties are now commonly labelled as simply "mixes".) The container volume must be at least 85% filled, and the label must state whether any peanuts are unblanched or of the Spanish variety.[1]

The most detailed section deals with weight percentages:

"Each such kind of nut ingredient when used shall be present in a quantity not less than 2 percent and not more than 80 percent by weight of the finished food."[1]

Furthermore, if a variety X exceeds 50%, the label must conspicuously state "contains up to 60% X", and so on in 10% increments up to 80%. (The first example given by the FDA is "contains up to 60% pecans".) When testing mixed nuts for compliance, the FDA samples at least 24 pounds to reduce sampling error.