U = {a, b, c, d, e, f, g, h}
(i) A = {a, b, c}
A' = {d,e,f,g,h}
(ii) B = {d, e, f, g}
∴ B' = {a, b , c , h}
(iii) C = {a, c, e, g}
∴ C' = {b, d, f, h}
(iv) D = {f, g, h, a}
∴ D' = {b, c,d,e}
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.
Find the mean deviation about the median for the data
xi | 15 | 21 | 27 | 30 | 35 |
fi | 3 | 5 | 6 | 7 | 8 |
The complement of a set is described as A’ = {x: x ∈ U and x ∉ A}
where,
A’ stands for the complement.
1. Complement Laws: The union of a set A and its complement A’ allows the universal set U of which, A and A’ are a subset.
A ∪ A’ = U
Also, the intersection of a set A and its complement A’ cause the empty set ∅.
A ∩ A’ = ∅
For Example: If U = {11, 12 , 13 , 14 , 15 } and A = {11 , 12 , 13 } then A’ = {14 , 15}. From this it can be seen that
A ∪ A’ = U = { 11 , 12 , 13 , 14 , 15}
Also, A ∩ A’ = ∅
2. Law of Double Complementation: According to the law, if we take the complement of the complemented set A’ then, we get the set A itself.
(A’)’ = A
In the previous example we can see that, if U = {11 , 12 , 13 , 14 , 15} and A = {11 , 12, 13} then A’ ={14 , 15}. Now if we consider the complement of set ‘A’ we get,
(A’)’ = {11 , 12 , 13} = A
This gives back the set A itself.
3. Law of empty set and universal set: According to this law the complement of the universal set gives us the empty set and vice-versa i.e.,
∅’ = U And U’ = ∅
This law is accessible.