Test: Number Set Theory - Grade 12 MCQ

The set S consists of the square of an integer less than 10.

Power set P ({0, 1, 2}) is the set of all subsets of {0, 1, 2}. Hence, P({0, 1, 2}) = {null, {0}, {1}, {2}, {0, 1}, {0,2}, {1, 2}, {0, 1, 2}}.

The set of positive integers is not finite.

Two set are equal if and only if they have the same elements.

Set S of odd positive an odd integer less than 10 is {1, 3, 5, 7, 9}. Then, Cardinality of set S = |S| which is 5.

A subset R of the Cartesian product A x B is a relation from the set A to the set B.

Power set of null set has exactly one subset which is empty set.

Odd numbers less than 10 is {1, 3, 5, 7, 9}.

By the definition of set.

CONCEPT:
Power Set:
Let A be a set, then the set of all the possible subsets of A is called the power set of A and is denoted by P(A).
Note: If A is a finite set with m elements. Then the number of elements (cardinality) of the power set of A is given by: n (P(A)) = 2^m.
CALCULATION:
Given: A = {1, 3, 5}
Here, we have to find the cardinality of the power set of A i.e n (P(A))
As we know that if A is a finite set with m elements. Then the number of elements (cardinality) of the power set of A is given by: n (P(A)) = 2m.
Here, we can see that, the given A has 3 elements i.e n(A) = 3
So, the cardinality of the given set is n(P(A)) = 2³ = 8
Hence, the correct option is d.