Question

Answer ALL the questions. Each carriers ONE mark.
1. Define Power set.
2. Define infinite set? Give an example of finite set.
į502
3. Find the value of
į416'
4. Find the conjugate of z = 5i - 3
5. Express (-5i) (i) in the form of a+ib.
6. Write the first three terms of an = n(n + 2).
7. If an = 4n – 3, find (17.
8. If P = {1,2} find P x P x P.
lim
ate​

Answer 1

Step-by-step explanation:

S = {1, 2, 3}

P(S) = {ɸ, {1}, {2}, {3} {1,2}, {1,3}, {2,3}, {1,2,3}}

Number of Elements in Power Set –

For a given set S with n elements, number of elements in P(S) is 2^n. As each element has two possibilities (present or absent}, possible subsets are 2×2×2.. n times = 2^n. Therefore, power set contains 2^n elements.

Note –

Power set of a finite set is finite.

Set S is an element of power set of S which can be written as S ɛ P(S).

Empty Set ɸ is an element of power set of S which can be written as ɸ ɛ P(S).

Empty set ɸ is subset of power set of S which can be written as ɸ ⊂ P(S).

Let us discuss the questions based on power set.

Q1. The cardinality of the power set of {0, 1, 2 . . ., 10} is _________.

(A) 1024

(B) 1023

(C) 2048

(D) 2043