Which of the following are examples of the null set
(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) {x:x is a natural numbers, x < 5 and x > 7 }
(iv) {y:y is a point common to any two parallel lines}
(i) A set of odd natural numbers divisible by 2 is a null set because no odd number is divisible by 2.
(ii) A set of even prime numbers is not a null set because 2 is an even prime number.
(iii) {x: x is a natural number, x < 5 and x > 7} is a null set because a number cannot be simultaneously less than 5 and greater than 7.
(iv) {y: y is a point common to any two parallel lines} is a null set because parallel lines do not intersect. Hence, they have no common point.
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Hey! So let's go through each of these one by one and figure out which are examples of the null set. A null set just means a set that has no elements in it — like it's totally empty.
Okay, first one: the set of odd natural numbers divisible by 2. That doesn't make sense, right? Because if a number is divisible by 2, it’s even, not odd. So there are no odd natural numbers divisible by 2. That makes this a null set.
Next, the set of even prime numbers. Well, 2 is the only even prime number. So this set has one element, which is 2. Since it’s not empty, it’s not a null set.
Now the third one: {x : x is a natural number, x < 5 and x > 7}. That’s impossible. A number can’t be less than 5 and greater than 7 at the same time. So no number fits that condition. That means this one is a null set too.
Last one: {y : y is a point common to any two parallel lines}. Parallel lines never meet, right? So they don’t have any points in common. That means this set also has no elements. So yeah, this one’s a null set as well.
So in the end, the null sets are (i), (iii), and (iv).
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Alright, let’s figure out which of these sets are empty, meaning they have no elements at all.
First up, odd natural numbers that are divisible by 2. Since any number divisible by 2 has to be even, there’s no way for it to be odd at the same time. So this set doesn’t have any numbers in it — it’s empty, or a null set.
Next, even prime numbers. The number 2 is even and also prime, so it belongs in this set. That means this set isn’t empty, so it’s not a null set.
Then we have natural numbers that are less than 5 and greater than 7 at the same time. That can’t happen because a number can’t be both smaller than 5 and bigger than 7 simultaneously. So there’s no number here either — another null set.
Finally, points that are common to two parallel lines. Since parallel lines never cross, they don’t share any points, which means this set has no elements. So, it’s a null set too.
To sum up, sets (i), (iii), and (iv) are null sets because they have no elements at all.
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odd natural numbers that are divisible by 2. Since any number divisible by 2 has to be even, there’s no way for it to be odd at the same time. So this set doesn’t have any numbers in it — it’s empty, or a null set.
Next, even prime numbers. The number 2 is even and also prime, so it belongs in this set. That means this set isn’t empty, so it’s not a null set.
Then we have natural numbers that are less than 5 and greater than 7 at the same time. That can’t happen because a number can’t be both smaller than 5 and bigger than 7 simultaneously. So there’s no number here either — another null set.
Finally, points that are common to two parallel lines. Since parallel lines never cross, they don’t share any points, which means this set has no elements. So, it’s a null set too.
To sum up, sets (i), (iii), and (iv) are null sets because they have no elements at all.
odd natural numbers that are divisible by 2. Since any number divisible by 2 has to be even, there’s no way for it to be odd at the same time. So this set doesn’t have any numbers in it — it’s empty, or a null set.
Next, even prime numbers. The number 2 is even and also prime, so it belongs in this set. That means this set isn’t empty, so it’s not a null set.
Then we have natural numbers that are less than 5 and greater than 7 at the same time. That can’t happen because a number can’t be both smaller than 5 and bigger than 7 simultaneously. So there’s no number here either — another null set.
Finally, points that are common to two parallel lines. Since parallel lines never cross, they don’t share any points, which means this set has no elements. So, it’s a null set too.
To sum up, sets (i), (iii), and (iv) are null sets because they have no elements at all.
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