Answer
Verified
411.3k+ views
Hint:To find a complement of a set, we subtract or remove its element from the universal set. The given sets are written in set builder notation; write it in roster notation to get clearer image in solving the question.
Complete step by step solution:
To solve this question, we will first elaborate the given data in the question. U is the universal set given in which all the alphabets of English are present and A is a set of all vowels in the English alphabets, in this manner we can say that A is a subset or a proper subset of the universal set U.
We can write this all in roster notation as follows
\[
{\text{U}} = \{ {\text{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}}\} \\
{\text{A}} = \{ {\text{a,}}\;{\text{e,}}\;{\text{i,}}\;{\text{o,}}\;{\text{u}}\} \\
\]
Now coming to the question, we have to find A’ and (A’)’, that is complement of A and A’ respectively.
Complement of a set is the set resulting from removal of the given set from the universal set.
According to this, A’ will be given as
\[
{\text{A'}} = {\text{U}} - {\text{A}} = \{ {\text{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x,
y, z}}\} - \{ {\text{a,}}\;{\text{e,}}\;{\text{i,}}\;{\text{o,}}\;{\text{u}}\} \\
{\text{A'}} = \{ {\text{b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z}}\} \\
\]
And (A’)’ will be given as
\[
{\text{(A')'}} = {\text{U}} - {\text{A'}} = \{ {\text{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w,
x, y, z}}\} - \\
\{ {\text{b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z}}\} \\
{\text{(A')'}} = \{ {\text{a,}}\;{\text{e,}}\;{\text{i,}}\;{\text{o,}}\;{\text{u}}\} \\
\]
Additional information: Complement of the universal set gives null set and also vice versa.
Note: U is denoted as the universal set. If we find a complement of a set then we will eventually get the set itself whose complement we have taken, it works just as negative of a negative equals positive. This question can also be solved with the help of Venn diagrams, try to solve it by yourself.
Complete step by step solution:
To solve this question, we will first elaborate the given data in the question. U is the universal set given in which all the alphabets of English are present and A is a set of all vowels in the English alphabets, in this manner we can say that A is a subset or a proper subset of the universal set U.
We can write this all in roster notation as follows
\[
{\text{U}} = \{ {\text{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}}\} \\
{\text{A}} = \{ {\text{a,}}\;{\text{e,}}\;{\text{i,}}\;{\text{o,}}\;{\text{u}}\} \\
\]
Now coming to the question, we have to find A’ and (A’)’, that is complement of A and A’ respectively.
Complement of a set is the set resulting from removal of the given set from the universal set.
According to this, A’ will be given as
\[
{\text{A'}} = {\text{U}} - {\text{A}} = \{ {\text{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x,
y, z}}\} - \{ {\text{a,}}\;{\text{e,}}\;{\text{i,}}\;{\text{o,}}\;{\text{u}}\} \\
{\text{A'}} = \{ {\text{b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z}}\} \\
\]
And (A’)’ will be given as
\[
{\text{(A')'}} = {\text{U}} - {\text{A'}} = \{ {\text{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w,
x, y, z}}\} - \\
\{ {\text{b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z}}\} \\
{\text{(A')'}} = \{ {\text{a,}}\;{\text{e,}}\;{\text{i,}}\;{\text{o,}}\;{\text{u}}\} \\
\]
Additional information: Complement of the universal set gives null set and also vice versa.
Note: U is denoted as the universal set. If we find a complement of a set then we will eventually get the set itself whose complement we have taken, it works just as negative of a negative equals positive. This question can also be solved with the help of Venn diagrams, try to solve it by yourself.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE