Question

List all the proper subsets of A = {0, 1, 2, 3}​

Answer 1

Hint:

For two sets A and B, A is said to be a proper subset of B, when A is a subset of B, but is not identical with B. Mathematically, we can express it as,

A ⊂ B when A ⊆ B but A ≠ B

Step-by-step explanation:

The given set is A = {0, 1, 2, 3}

Its subsets are { }, {0}, {1}, {2}, {3}, {0, 1}, {0, 2}, {0, 3}, {1, 2}, {1, 3}, {2, 3}, {0, 1, 2}, {0, 1, 3}, {0, 2, 3}, {1, 2, 3} and {0, 1, 2, 3}.

Of the above subsets, {0, 1, 2, 3} = A, but the rests do not. So to find the proper subsets, we do not take {0, 1, 2, 3}.

Thus the proper subsets are { }, {0}, {1}, {2}, {3}, {0, 1}, {0, 2}, {0, 3}, {1, 2}, {1, 3}, {2, 3}, {0, 1, 2}, {0, 1, 3}, {0, 2, 3} and {1, 2, 3}.