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National High School Mathematics League
1993 National High School Mathematics League
1
Problem of "0+0=0"
Problem of "0+0=0"
Source: 1993 National High School Mathematics League, Exam One, Problem 1
February 27, 2020
Problem Statement
If
M
=
{
(
x
,
y
)
∣
∣
tan
π
x
∣
+
sin
2
π
x
=
0
}
,
N
=
{
(
x
,
y
)
∣
x
2
+
y
2
≤
2
}
M=\{(x,y)||\tan\pi x|+\sin^2\pi x=0\},N=\{(x,y)|x^2+y^2\leq2\}
M
=
{(
x
,
y
)
∣∣
tan
π
x
∣
+
sin
2
π
x
=
0
}
,
N
=
{(
x
,
y
)
∣
x
2
+
y
2
≤
2
}
, then
∣
M
∩
N
∣
|M\cap N|
∣
M
∩
N
∣
is equal to
(A)
4
(B)
5
(C)
8
(D)
9
\text{(A)}4\qquad\text{(B)}5\qquad\text{(C)}8\qquad\text{(D)}9
(A)
4
(B)
5
(C)
8
(D)
9
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