P and Q are subsets of the universal set U defined as
U={x:x is an integer and 1<x<15}
P={x:x is odd} and Q={x:x is prime}
Find n(P¹n Q¹)
Ah, let me put on my mathematician clown nose for this one! Okay, so first we need to find the complement of P (P¹) and the complement of Q (Q¹).
P: {x:x is odd}
The complement of P (P¹) would be the set of all even numbers in the universal set U. So P¹ would be {x:x is even}.
Q: {x:x is prime}
The complement of Q (Q¹) would be the set of all non-prime numbers in the universal set U. So Q¹ would be {x: x is composite}.
Now, we need to find the intersection of P¹ and Q¹ (P¹n Q¹).
P¹n Q¹ would be the set of numbers that are both even and composite. Since the universal set U is defined as integers between 1 and 15, the numbers that fulfill both conditions are 4, 6, 8, 9, 10, 12, and 14.
So, n(P¹n Q¹) is 7.
Remember, laughter is the best math-solving companion!
To find n(P¹n Q¹) (the number of elements in the intersection of the complements of sets P and Q), we need to determine the complement sets of P and Q.
Let's start by finding the complement of set P (P').
The set P contains all odd numbers in the range (1, 15). So, the complement of P (P') would consist of all the even numbers in the range (1, 15).
P' = {x: x is even}
Next, let's find the complement of set Q (Q').
The set Q contains all prime numbers in the range (1, 15). So, the complement of Q (Q') would contain all the non-prime numbers in the range (1, 15).
Q' = {x: x is non-prime}
Now, to find the intersection of P' and Q', we can simply find all the elements that are common to both sets.
P' ∩ Q' = {x: x is even and x is non-prime}
Since all even numbers are non-prime, we can say that P' ∩ Q' is equal to the set of all even numbers in the range (1, 15).
Therefore, n(P' ∩ Q') will be equal to the number of elements in the set {2, 4, 6, 8, 10, 12, 14}, which is 7.
Hence, n(P¹n Q¹) = 7.
To find n(P¹n Q¹), we need to determine the elements that are not common to sets P and Q.
Set P contains all odd integers between 1 and 15, while set Q contains all prime integers between 1 and 15.
First, let's find the elements that are not in P. To do this, we need to determine the even integers between 1 and 15. The even integers are: 2, 4, 6, 8, 10, 12, and 14. None of these are in set P, so we keep them for further calculations.
Next, let's find the elements that are not in Q. To do this, we need to determine the composite (non-prime) integers between 1 and 15. The composite integers are: 4, 6, 8, 9, 10, 12, and 14. None of these are in set Q, so we keep them as well.
Now, we need to find the intersection (or common elements) of the two sets of integers: {2, 4, 6, 8, 10, 12, 14}. Since none of these are in both sets P and Q, the intersection is empty.
Finally, we find n(P¹n Q¹), which represents the number of elements in the intersection we found. In this case, the intersection is empty, so n(P¹n Q¹) is 0.
Not odd, nor prime. 4,6,8,10,12,14 which means even but not prime.
I assume (P¹n Q¹) reads not P and not Q