Taking the set of natural numbers as the universal set, write down the complements of the following sets: (vii) $\{ x : x$ is a perfect cube\}

If $A = \{x : x$ is a natural number \}, $B = \{x : x$ is an even natural number\} $C = \{x : x$ is an odd natural number\} and $D = \{x : x$ is a prime number \}, find (vi) $C \cap D$

Write the following as intervals : (ii) \{$x : x \in R, – 12 < x < –10$\}

Examine whether the following statements are true or false: (i) \{ a, b \} $\not\subset$ \{ b, c, a \}

If $A = \{1, 2, 3, 4\}$, $B = \{3, 4, 5, 6\}$, $C = \{5, 6, 7, 8 \}$and $D = \{ 7, 8, 9, 10 \}$; find (ii) $A \cup C$

Find sets $A, B$ and $C$ such that $A \cap B, B \cap C$ and $A \cap C$ are non-empty sets and $A \cap B \cap C = \phi$.

Fill in the blanks to make each of the following a true statement : (ii) $\phi′ \cap A = . . .$

Taking the set of natural numbers as the universal set, write down the complements of the following sets: (i) $\{x : x$ is an even natural number\}

If $A = \{ 3, 5, 7, 9, 11 \}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (x) $( A \cup D) \cap ( B \cup C)$

Let $A = \{ 1, 2, \{ 3, 4 \}, 5 \}$. Which of the following statements are incorrect and why? (i) \{3, 4\} $\subset$ $A$

State whether each of the following set is finite or infinite: (ii) The set of letters in the English alphabet

Let $A = \{ 1, 2, \{ 3, 4 \}, 5 \}$. Which of the following statements are incorrect and why? (xi) \{$\phi$\} $\subset$ $A$

Write the following sets in the set-builder form : (i) $\{3, 6, 9, 12\}$

If $A = \{x : x$ is a natural number \}, $B = \{x : x$ is an even natural number\} $C = \{x : x$ is an odd natural number\} and $D = \{x : x$ is a prime number \}, find (v) $B \cap D$

Write the following as intervals : (i) \{$x : x \in R, – 4 < x \le 6$\}

Write down all the subsets of the following sets (i) \{a\}

If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (xii) $D – C$

If $A = \{x : x$ is a natural number \}, $B = \{x : x$ is an even natural number\} $C = \{x : x$ is an odd natural number\} and $D = \{x : x$ is a prime number \}, find (i) $A \cap B$

Fill in the blanks to make each of the following a true statement : (i) $A \cup A′ = . . .$

List all the elements of the following sets : (ii) $B = \{x : x$ is an integer, $– \frac{1}{2} < x < \frac{9}{2}\}$