问题 选择题
有下列四种说法:
①“若am2<bm2,则a<b”的逆命题为真;
②“命题p∨q为真”是“命题p∧q为真”的必要不充分条件;
③命题“∃x0∈R使得x2-x>0”的否定是“∀x∈R都有x2-x≤0”;
④若实数x,y∈[0,1],则满足:x2+y2<1的概率为
π
4

其中正确命题的个数是(  )
A.0B.1C.2D.3
答案

①“若am2<bm2,则a<b”的逆命题是“若a<b,则am2<bm2”,

∵当m=0时不成立,∴①是假命题;

②∵“命题p∨q为真”是指命题p,q中至少有一个是真命题,

“命题p∧q为真”是指p,q都是真命题,故②是真命题;

③∵命题“∃x0∈R使得x2-x>0”是特称命题,

∴它的否定是“∀x∈R都有x2-x≤0”,故③是真命题;

④∵实数x,y∈[0,1],∴区域面积为1,

x2+y2<1的面积=

π
4

∴若实数x,y∈[0,1],则满足:x2+y2<1的概率为

π
4
.故④是真命题.

故选D.

单项选择题
问答题

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