The number of solutions to {1,2} X{1,2,3,4,5}, where X is a subset of {1,2,3,4,5}, is:

1972 AMC 12 Problem 4

Attempt Problem 4 of the 1972 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1972 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The number of solutions to

\{1,2\}\subseteq X\subseteq\{1,2,3,4,5\},

where

X

is a subset of

\{1,2,3,4,5\},

is:

2

4

6

8

None of these

The elements

1

and

2

are forced

Each of

3,4,5

may independently be included or omitted

Every valid

X

contains

1,2,

while each of

3,4,5

may be chosen independently. Hence there are

2^3=8

possible sets.

Therefore, the correct answer is D.