Determing which sets are subsets of each other

Question

I am in first year discrete math or key concepts is what it is called , i have a question about sets that states " suppose that $A=\{2,3,4,7\},B=\{3,7\},C=\{2,4,7\},D=\{3,5,7\}$. Determine which of these sets are subsets of which other of these sets. "

This may be a simple question for some but I am not understanding the concept and could use some help!

TIA

score 2 · Answer 1 · edited Oct 18 '18 at 02:43

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Basically $A \subset B $ iff $ x \in A \rightarrow x \in B $, which means "set A is a subset of B if and only if the presence of x in set A implies that x is in set B."* Can you take it from there?

*The "iff" means that if the left side is true, then the right side is true, and if the right side is true, then the left side is also true. In this case, the right side is the full statement $ x \in A \rightarrow x \in B $ which is logical implication: for this statement as a whole to be true, if $x \in A$, we must have $x \in B$; if $x \not\in A$, then x can be in B or not, it doesn't matter, and the statement is still true. Otherwise, if $x \in A$ but $x \not\in B$, the statement is false.

edited Oct 18 '18 at 02:43

Russ

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answered Oct 18 '18 at 01:59

gary

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okay I think I understand , as long as one set has all the numbers of another it is a subset? correct? – Breanna Oct 18 '18 at 02:04
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thank you for the clarification as well! – Breanna Oct 18 '18 at 02:08
If set A has all the numbers of set B, then B is a subset of A. If A has some additional numbers not in B, then B is a proper subset, denoted "$\subset$", of A; if B $\subset$ A and A and B could be equal, then we write this as A $\subseteq$ B. – Russ Oct 18 '18 at 02:13
@Breanna: Precisely. A is contained in B if every thing that is A is in B. – gary Oct 18 '18 at 02:16
Moreover, as another (non-) example: $ {1,4} \notsubset {1,2,3}$. – gary Oct 18 '18 at 02:24
@Russ: Thanks for the add-ons. – gary Oct 18 '18 at 18:59

irchans · Answer 2 · 2018-10-18T02:36:21.033

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B is a subset of D because every element of B is in D.

3 is in D

7 is in D

D is not a subset of B because 5 is not an element of B.

edited Oct 18 '18 at 02:36

answered Oct 18 '18 at 01:59

irchans

1,915

would that mean that C is subset of A then? – Breanna Oct 18 '18 at 02:01
Yes ! C is a subset of A ! – irchans Oct 18 '18 at 02:07
awesome thanks for the clarification ! much appreciated – Breanna Oct 18 '18 at 02:08

Determing which sets are subsets of each other

2 Answers2