性能，価格，デザインを重視する人の集合を，それぞれ，集合“性能”，集合“価格”，集合“デザイン”として，図2のベン図で表す。次の命令の条件に合致するベン図中の領域はどれか。
件数表示（[[性能=1] or [価格=1]] and [デザイン=1]）
出典 平成27年度 春期 ITパスポート試験 問98
解説
問 98
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×Incorrectア
A, B, E is the region of “people who value performance or price but do not value design”, that is, [[Performance=1] or [Price=1]] and [Design=0]. It collects only the parts outside the Design circle, which is the opposite of [Design=1] in the condition, so it is wrong.
×Incorrectイ
A is a region not contained in the Design circle (valuing performance only), so it does not satisfy [Design=1]. In addition, D, which is the region valuing all three, is missing, and D also satisfies the condition with Performance=1 and Design=1, so this set has both an extra item and a missing item.
×Incorrectウ
B, D is the overlapping part of the Performance circle and the Price circle, that is, the region [Performance=1] and [Price=1]. However, the condition in the question joins performance and price with or (either one is enough), not with and. Furthermore, B is outside the Design circle, so it does not satisfy [Design=1] either.
○エ
正解In the Venn diagram of Figure 2, the regions occupied by each set are as follows: the set “Performance” (the upper circle) = A, B, C, D; the set “Price” (the lower-left circle) = B, D, E, F; the set “Design” (the lower-right circle) = C, D, F, G. The condition of the command is [[Performance=1] or [Price=1]] and [Design=1], so we evaluate it starting from the inner or. First, “Performance=1 or Price=1” is the union of the Performance circle and the Price circle, which is A, B, C, D, E, F. Next, this is joined with “Design=1” by and (intersection), so out of the region obtained above only the parts that are also inside the Design circle remain, giving C, D, F. In meaning, this is the region of “people who value design and also value at least one of performance or price”, where C = valuing performance and design, F = valuing price and design, and D = valuing all three. Therefore the correct answer is エ (C, D, F).
ここがポイント
In a Venn diagram, and (logical conjunction) corresponds to the overlap of regions (intersection), and or (logical disjunction) corresponds to the combined range of regions (union). For a conditional expression, find the regions in order starting from the innermost parentheses.
Organize the regions formed by the three circles according to “which sets they belong to”. Here, Performance={A,B,C,D}, Price={B,D,E,F}, Design={C,D,F,G}, and the central D belongs to all three sets, so be careful not to miss counting it even under an and condition.