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EXAMPLE 1: Let set A = {1,2,3} and B = {1,2,3,4,5}. Since all the elements of set A are in set B, then we can say that A is a subset of B (in symbol A (subseteq) B). On the other hand, B is not a subset of set A since 4 and 5 are not in set A. EXAMPLE 2: Determine all the possible subsets of the set. a. {a, b} b. {1, 2, 3} SOLUTION: a. Note that every set is a subset of itself. Thus, {a,b} is a subset. We also note that the empty set is the subset of all sets, so we have {} as a subset. The other subsets are {a} and {b}. The complete list of subsets of {a, b} is {a,b}, {}, {a}, {b}. b. Since the set {1, 2, 3} contains three elements, we would have the following:

          EXAMPLE 1:
Let set A = {1,2,3} and B = {1,2,3,4,5}. Since all the elements of set A are in set B, then we can say that A is a subset of B (in symbol A (subseteq) B). On the other hand, B is not a subset of set A since 4 and 5 are not in set A.
EXAMPLE 2:
Determine all the possible subsets of the set.
a. {a, b}
b. {1, 2, 3}
SOLUTION:
a. Note that every set is a subset of itself. Thus, {a,b} is a subset. We also note that the empty set is the subset of all sets, so we have {} as a subset. The other subsets are {a} and {b}. The complete list of subsets of {a, b} is
{a,b}, {}, {a}, {b}.
b. Since the set {1, 2, 3} contains three elements, we would have the following:

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EXAMPLE 1:
Let set A = 1,2,3 and B = 1,2,3,4,5. Since all the elements of set A are in set B, then we can say that A is a subset of B (in symbol A (subseteq) B). On the other hand, B is not a subset of set A since 4 and 5 are not in set A.
EXAMPLE 2:
Determine all the possible subsets of the set.
a. a, b
b. 1, 2, 3
SOLUTION:
a. Note that every set is a subset of itself. Thus, a,b is a subset. We also note that the empty set is the subset of all sets, so we have as a subset. The other subsets are a and b. The complete list of subsets of a, b is
a,b, , a, b.
b. Since the set 1, 2, 3 contains three elements, we would have the following:

Added by Jose Carlos G.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Rebecca Belvin

09/03/2023

Step 1

Set A is a subset of set B because all the elements in set A are also in set B. This means that every element in set A is also in set B. Show more…

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Elements of set A are . and B = {0,1,2,3,4,5}. Since all the elements in set A are also in set B, we can say that A is a subset of B. However, the elements in set B that are not in set A means that B is not a subset of A. EXAMPLE 2: Determine all the possible subsets of the set {a, b} {1,2,3}. SOLUTION: {a, b} is a subset of itself. Thus, {a, b} is a subset. We also note that the empty set {} is a subset. The other subsets are {a}, {b}, and {a, b}. Since the set {1,2,3} contains three elements, we would have the following subsets: {} {1} {2} {3} {1,2} {1,3} {2,3} {1,2,3}

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Transcript

00:01 Okay, this problem is just examples, so i'm just going to go through the examples and explain it to you.

00:08 The first question we're given a and b sets a and b, and i want to know first of all, is a a subset of b? in order for a to be a subset of b, every element in a has to be in b.

00:27 So in a, i've got a 1, and i've got a 1 there.

00:31 I've got a 2, and i've got a 2 there.

00:34 I've got a 3, and i've got a 3 there.

00:36 So yes, a is a subset of b.

00:40 Next it says, is b a subset of a? well in this case, everything in b has to be in a.

01:02 Alright, in b, i've got 1, and there's a 1.

01:06 I've got 2, and there's a 2.

01:08 I've got 3, and there's a 3.

01:10 But i've got a 4 and a 5 that's not there.

01:15 So no.

01:18 So you've got to look at the first set first, and everything in that set has to be in the second one.

01:26 Okay, on example 2, we're supposed to give all the possible subsets of a, b.

01:37 Okay, so we're supposed to list all the subsets.

01:40 First of all, always start with the empty set.

01:44 Okay, and there's a systematic way to go about this.

01:48 This is the set that contains no elements.

01:53 So now let's list all the sets that contain one element, not one set, one element.

02:03 Okay, so it'd be a and then b.

02:10 Alright, and then two elements.

02:12 Well there's only one, and it's ab...

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