consider the following and 1a b c a b a c and 2a 223026529

Consider the following :
$$\eqalign{ & 1.\,\,A \cup \left( {B \cap C} \right) = \left( {A \cap B} \right) \cup \left( {A \cap C} \right) \cr & 2.\,\,A \cap \left( {B \cup C} \right) = \left( {A \cup B} \right) \cap \left( {A \cup C} \right) \cr} $$
Which of the above is/are correct ?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Answer : Neither 1 nor 2

Solution :
According to 'Distribution law' in set theory the given both statements are wrong.
Statement 1 - Distribution law
Statement 2 - Distribution law

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

View Answer

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. $$1 - \sqrt 5 - \sqrt 2 + \sqrt {10} $$

View Answer

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

View Answer

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

View Answer

Consider the following :
$$\eqalign{ & 1.\,\,A \cup \left( {B \cap C} \right) = \left( {A \cap B} \right) \cup \left( {A \cap C} \right) \cr & 2.\,\,A \cap \left( {B \cup C} \right) = \left( {A \cup B} \right) \cap \left( {A \cup C} \right) \cr} $$
Which of the above is/are correct ?

Releted MCQ Question on
Calculus >> Sets and Relations

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

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

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

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

Practice More Releted MCQ Question on
Sets and Relations

Practice More MCQ Question on Maths Section

Consider the following : $$\eqalign{ & 1.\,\,A \cup \left( {B \cap C} \right) = \left( {A \cap B} \right) \cup \left( {A \cap C} \right) \cr & 2.\,\,A \cap \left( {B \cup C} \right) = \left( {A \cup B} \right) \cap \left( {A \cup C} \right) \cr} $$ Which of the above is/are correct ?

Releted MCQ Question on Calculus >> Sets and Relations

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

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

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

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

Practice More Releted MCQ Question on Sets and Relations

Practice More MCQ Question on Maths Section

Consider the following :
$$\eqalign{ & 1.\,\,A \cup \left( {B \cap C} \right) = \left( {A \cap B} \right) \cup \left( {A \cap C} \right) \cr & 2.\,\,A \cap \left( {B \cup C} \right) = \left( {A \cup B} \right) \cap \left( {A \cup C} \right) \cr} $$
Which of the above is/are correct ?

Releted MCQ Question on
Calculus >> Sets and Relations

Practice More Releted MCQ Question on
Sets and Relations