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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}

Comments for Finite Subsets

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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


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