# Finite Subsets

Which of the following are subsets of {a, b, c}

Select all that apply.
(a) bc
(b) {b, c}
(c) {c}
(d) {b}
(e) ab
(f) {}
(g) {a}
(h) a
(i) ac
(j) b
(k) c
(l) abc
(m) {a, b}
(n) {a, c}
(o) {a, b, c}

 Jan 26, 2011 Finite Subsets by: Staff The question: Which of the following are subsets of {a, b, c} Select all that apply. (a) bc (b) {b, c} (c) {c} (d) {b} (e) ab (f) {} (g) {a} (h) a (i) ac (j) b (k) c (l) abc (m) {a, b} (n) {a, c} (o) {a, b, c} The answer: A “subset” ⊆ and a “proper subset”⊂ are not equivalent to each other. “Proper Subset” ⊂: Every element (without exception) contained in a subset is also contained in the other set. . . . AND, the subset CANNOT BE EQUAL to the original set. For example, if set A = {1,10,11,50) and set B = {10,11), then set B is a “proper subset” of set A. B ⊂A, B is a “proper subset” of A “Subset” ⊆: Every element (without exception) contained in a subset is also contained in the original set. . . . AND, the subset CAN BE EQUAL to the original set. For example, if set A = {1,10,11,50) and set C = {1,10,11,50), then set C is a “subset” of set A. C ⊆A, C is a “subset” of A , even though it is equal to set A Since your question specifically asks to identify which choices on your list are subsets (not proper subsets), I am going to use the definition of “subset” ⊆ as the criteria. (a) bc – NOT A SUBSET. To be a subset it should be written {b,c} (b) {b, c} – YES (c) {c} – YES (d) {b} – YES (e) ab – NOT A SUBSET. To be a subset it should be written {a,b} (f) {} – YES, an empty set is a subset of {a, b, c} (g) {a} – YES (h) a – NOT A SUBSET. To be a subset it should be written {a} (i) ac – NOT A SUBSET. To be a subset it should be written {a,c} (j) b – NOT A SUBSET. To be a subset it should be written {b} (k) c – NOT A SUBSET. To be a subset it should be written {c} (l) abc – NOT A SUBSET. To be a subset it should be written {a,b,c} (m) {a, b} – YES (n) {a, c} – YES (o) {a, b, c} – YES, a subset, but not a proper subset Thanks for writing. Staff www.solving-math-problems.com