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National High School Mathematics League
1998 National High School Mathematics League
2
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Set Problem
Source: 1998 National High School Mathematics League, Exam One, Problem 2
March 8, 2020
Problem Statement
Nonempty set
A
=
{
x
∣
2
a
+
1
≤
x
≤
3
a
−
5
}
,
B
=
{
x
∣
3
≤
x
≤
22
}
A=\{x|2a+1\leq x\leq 3a-5\},B=\{x|3\leq x\leq22\}
A
=
{
x
∣2
a
+
1
≤
x
≤
3
a
−
5
}
,
B
=
{
x
∣3
≤
x
≤
22
}
, then the range value of
a
a
a
such that
A
⊆
A
∩
B
A\subseteq A\cap B
A
⊆
A
∩
B
is
(A)
{
a
∣
1
≤
a
≤
9
}
(B)
{
a
∣
6
≤
a
≤
9
}
(C)
{
a
∣
a
≤
9
}
(D)
∅
\text{(A)}\{a|1\leq a \leq9\}\qquad\text{(B)}\{a|6\leq a \leq9\}\qquad\text{(C)}\{a|a \leq9\}\qquad\text{(D)}\varnothing
(A)
{
a
∣1
≤
a
≤
9
}
(B)
{
a
∣6
≤
a
≤
9
}
(C)
{
a
∣
a
≤
9
}
(D)
∅
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