Choose the correct solution in roster form: Suppose X = {1, 2, 3, 4, 5, 6 } is the universal set and P =
{2, 4, 6}. What is P’?
a. {1,3}
b. {1,5}
c. {1,3,5}
d. {3,5}
I don't need you to tell me the answer but could you please tell me what the universal set means? so I can solve it on my own.
Thank you and have a great day. :)
In any particular question dealing with sets, the universal set is the
set within all dealings, discussion and/or calculations take place. You don't
consider any other elements except those of the universal set.
e.g. if your universal set is the set of integers, then addition, subtraction and
multiplication of any two elements will yield an element within that universal set.
However division between two elements of the universal set may yield results that are not in the universal set.
e.g. 5 and 3 are both elements of I, but 3/5 is not found in I (the integers)
so in your question we can only talk about the elements of {1, 2, 3, 4, 5, 6}
clearly P, which is {2,4,6} is a subset of X, since all the elements of P are found in X.
The notation P' means "not P", so it would be all those elements of X not stated in P
P' = {1, 3, 5}
Thank you so much I now understand this question so much better.
Of course! The universal set refers to the set that contains all the elements under consideration in a specific context. It is denoted by the letter U or sometimes by a specific name. In this case, the universal set is X = {1, 2, 3, 4, 5, 6}, which means that the elements 1, 2, 3, 4, 5, 6 are under consideration in the context of the problem. P' refers to the complement of set P, which consists of all the elements in the universal set that are not in set P. So, you need to find the elements in the universal set X that are not in P = {2, 4, 6}.
Of course! In set theory, a universal set is a set that contains all the elements under consideration. It is often denoted by the symbol "U" or sometimes "X".
In this case, the given universal set is X = {1, 2, 3, 4, 5, 6}, which means that this set contains all the elements that are being considered in the problem.
Now, let's move on to find P', which is called the complement of set P. The complement of a set contains all the elements from the universal set that are not in the given set.
The given set P = {2, 4, 6}, which means it contains the elements 2, 4, and 6 from the universal set X.
To find the complement P', we need to determine the elements in the universal set X that are not in set P. In other words, we need to find the elements in X which are not equal to 2, 4, or 6.
So, to find P', we look for the elements in X that are not in set P. From the given universal set X = {1, 2, 3, 4, 5, 6}, we can see that the elements 1, 3, and 5 are not in set P.
Hence, P' = {1, 3, 5}.
Now you can refer back to the choices and identify the correct answer based on this explanation. Feel free to let me know if you have any further questions. Have a great day too!