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Can you explain the answer of this question below:
Identify the null set from the following
- A:Odd natural numbers divisible by 2
- B:The set which contains only zero as its element
- C:The set of even prime numbers
- D:The set of points common to two intersecting lines
The answer is a.
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Can you explain the answer of this question below:Identify the null se...
Since none of the odd number is divisible by 2, so it would be a null set.
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Can you explain the answer of this question below:Identify the null se...
Identifying the Null Set
Definition: A null set is a set with no elements.
To identify a null set, we need to determine whether the set contains any elements. If there are no elements in the set, it is a null set.
a) Odd natural numbers divisible by 2
- Odd natural numbers are numbers that cannot be divided evenly by 2.
- If a number is divisible by 2, it means it can be divided evenly by 2.
- Therefore, the set of odd natural numbers divisible by 2 is a null set because there are no numbers that meet this criteria.
b) The set which contains only zero as its element
- This is a set with one element, which is zero.
- Therefore, this set is not a null set.
c) The set of even prime numbers
- Even numbers are numbers that can be divided evenly by 2.
- Prime numbers are numbers that only have two factors: 1 and itself.
- The only even prime number is 2.
- Therefore, the set of even prime numbers has one element, which is 2.
- This set is not a null set.
d) The set of points common to two intersecting lines
- Two intersecting lines have exactly one point in common.
- Therefore, the set of points common to two intersecting lines has one element.
- This set is not a null set.
Conclusion
The null set is a set with no elements. In this question, the null set is the set of odd natural numbers divisible by 2 because there are no numbers that meet this criteria. The other sets have at least one element and are not null sets.
Definition: A null set is a set with no elements.
To identify a null set, we need to determine whether the set contains any elements. If there are no elements in the set, it is a null set.
a) Odd natural numbers divisible by 2
- Odd natural numbers are numbers that cannot be divided evenly by 2.
- If a number is divisible by 2, it means it can be divided evenly by 2.
- Therefore, the set of odd natural numbers divisible by 2 is a null set because there are no numbers that meet this criteria.
b) The set which contains only zero as its element
- This is a set with one element, which is zero.
- Therefore, this set is not a null set.
c) The set of even prime numbers
- Even numbers are numbers that can be divided evenly by 2.
- Prime numbers are numbers that only have two factors: 1 and itself.
- The only even prime number is 2.
- Therefore, the set of even prime numbers has one element, which is 2.
- This set is not a null set.
d) The set of points common to two intersecting lines
- Two intersecting lines have exactly one point in common.
- Therefore, the set of points common to two intersecting lines has one element.
- This set is not a null set.
Conclusion
The null set is a set with no elements. In this question, the null set is the set of odd natural numbers divisible by 2 because there are no numbers that meet this criteria. The other sets have at least one element and are not null sets.
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Can you explain the answer of this question below:Identify the null se...
Because neither of the odd no. is divisible by 2 so it would be null set
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