Question

If the cardinality of a set $$A$$ is 4 and that of a set $$B$$ is 3, then what is the cardinality of the set $$A\Delta B\,?$$

A. 1
B. 5
C. 7
D. Cannot be determined as the sets $$A$$ and $$B$$ are not given  
Answer :   Cannot be determined as the sets $$A$$ and $$B$$ are not given
Solution :
Given, $$n\left( A \right) = 4,\,n\left( B \right) = 3$$
Since, the sets $$A$$ and $$B$$ are not known, then cardinality of the set $$A\Delta B$$  cannot be determined.

Releted MCQ Question on
Calculus >> Sets and Relations

Releted Question 1

If $$X$$ and $$Y$$ are two sets, then $$X \cap {\left( {X \cup Y} \right)^c}$$   equals.

A. $$X$$
B. $$Y$$
C. $$\phi $$
D. None of these
Releted Question 2

The expression $$\frac{{12}}{{3 + \sqrt 5 + 2\sqrt 2 }}$$    is equal to

A. $$1 - \sqrt 5 + \sqrt 2 + \sqrt {10} $$
B. $$1 + \sqrt 5 + \sqrt 2 - \sqrt {10} $$
C. $$1 + \sqrt 5 - \sqrt 2 + \sqrt {10} $$
D. $$1 - \sqrt 5 - \sqrt 2 + \sqrt {10} $$
Releted Question 3

If $${x_1},{x_2},.....,{x_n}$$    are any real numbers and $$n$$ is any positive integer, then

A. $$n\sum\limits_{i = 1}^n {{x_i}^2 < {{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$
B. $$\sum\limits_{i = 1}^n {{x_i}^2 \geqslant {{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$
C. $$\sum\limits_{i = 1}^n {{x_i}^2 \geqslant n{{\left( {\sum\limits_{i = 1}^n {{x_i}} } \right)}^2}} $$
D. none of these
Releted Question 4

Let $$S$$ = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of $$S$$ is equal to

A. 25
B. 34
C. 42
D. 41

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