I. A. List the elements of the following sets.
1. G= {x|x>8, x is an even integer}
2. E= {x|x is a subject in Grade 7}
3. 0= {x|x is a counting number between 100 and 105}
4. M= {x|x is a month with 28 days)
5. T is a set of colors of Olympic rings
B. Identify whether each statement is true or false. The symbol- denotes equivalence.
1. {T, O, P} = {P, O, T}
4. {ø} = { }
2. {A, L, O, N}~{L, O, A, N}
5. {solid, liquid, gas}~ {red, white, blue}
3. {2017} = {2, 0, 1, 7}
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Answer:
A. Listing the elements of the given sets:
1. \( G = \{x \mid x > 8, x \text{ is an even integer}\} \)
Elements: 10, 12, 14, ...
2. \( E = \{x \mid x \text{ is a subject in Grade 7}\} \)
Elements: Math, Science, English, ...
3. \( 0 = \{x \mid x \text{ is a counting number between 100 and 105}\} \)
Elements: 101, 102, 103, 104, 105
4. \( M = \{x \mid x \text{ is a month with 28 days}\} \)
Elements: February
5. \( T \) is a set of colors of Olympic rings
Elements: Blue, Yellow, Black, Green, Red
B. Identifying whether each statement is true or false:
1. \( \{T, O, P\} = \{P, O, T\} \) (True)
The order of elements in a set doesn't matter. Both sets contain the same elements.
2. \( \{\emptyset\} = \{\} \) (False)
The first set contains an empty set, while the second set is actually an empty set. They are not equivalent.
3. \( \{A, L, O, N\} \sim \{L, O, A, N\} \) (True)
The tilde symbol (\(\sim\)) signifies equivalence of sets, regardless of element order.
4. \( \{\text{solid, liquid, gas}\} \sim \{\text{red, white, blue}\} \) (False)
The two sets have different elements and thus are not equivalent.
5. \( \{2017\} = \{2, 0, 1, 7\} \) (False)
These sets are not equivalent as they have different elements. The first set contains a single element, 2017, while the second set contains four distinct elements.
Step-by-step explanation:
Answer:
1. True
2. True
3. True
4. True
5. True