2. 外语
  3. What is the number of integers that are common to both set S and set T? (1) The number of integers in S is 7，and the number of

What is the number of integers that are common to both set S and set T? (1) The number of integers in S is 7，and the number of

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问题 What is the number of integers that are common to both set S and set T?
(1) The number of integers in S is 7，and the number of integers in T is 6.
(2) U is the set of integers that are in S only or in T only or in both，and the number of integers in U is 10．
选项 A、Statement(1) ALONE is sufficient，but statement (2) alone is not sufficient．
B、Statement(2) ALONE is sufficient，but statement (1) alone is not sufficient．
C、BOTH statements TOGETHER are sufficient，but NEITHER statement ALONE is sufficient．
D、EACH statement ALONE is sufficient．
E、Statements(1) and(2) TOGETHER are NOT sufficient．
答案C
解析 In standard notation, S ∩ T and S ∪ T represent the intersection and union, respectively, of sets S and T, and |S| represents the number of elements in a set S. Determine | S ∩ T|.
(1)     It is given that | S| = 7 and | T |= 6. If, for example, S = {1,2,3,4,5,6,7} and T= {1,2,3,4,5,6},then | S ∩T |= 6. However, if S = {1,2,3,4,5,6,7,} and T= {11,12, 13,14,15,16}, then |S∩T| = 0; NOT sufficient.
(2)     It is given that | S ∪ T| = 10. If, for example, S = {1,2,3,4,5,6,7} and T= {1,2,3,8,9, 10}, then S∪T = {1,2,S,4,5,6,7,8,9, 10},| S∪T | = 10,and| S∩T | = 3. However, if 5 = {1,2,3,4,5,6,7} and T= {11,12,13}, then S∪T = {1,2,3, 4,5,6,7,11,12,13}, |S∪T|=10, and |S∩T| = 0; NOT sufficient.
Taking (1) and (2) together along with the general addition rule for two sets A and B (A∪B| = |A| + |B| - |A∩B|) applied to sets S and T gives 10 = 7 + 6-|5∩T|, from which | S ∩ T| can be determined.
The correct answer is C;
both statements together are sufficient.
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