Question

若集合P＝{x|x＝3m+1，m∈N}，Q＝｛y|y＝5n+2，n∈N｝，則P∩Q為

1. A.
   {z|z＝15k-7，k∈N}
2. B.
   {z|z＝15k-8，k∈N}
3. C.
   {z|z＝15k+8，k∈N}
4. D.
   {z|z＝15k+7，k∈N}

Answer 1

B
由于P∩Q，必有3m+1=5n+2即3m＝5n+1，所以5n+1是3的倍數，不妨設n=3k-2， 3k-1當 n＝ 3k- 2時 5n+1＝ 5(3k-2)+1＝15k-9當n＝3k-1時5n+1＝ 5(3k-1)+1＝15k-4∴5n+2＝15k-8或5n+2＝15k-3，后者舍去，∴Z＝15k-8