What universal set(s) would you propose for each of the following : (i) The set of right triangles.

State whether each of the following set is finite or infinite: (v) The set of circles passing through the origin (0,0)

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

Let $A, B$, and $C$ be the sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$. Show that $B = C$.

In the following, state whether $A = B$ or not: (iv) $A = \{ x : x$ is a multiple of 10\}, $B = \{ 10, 15, 20, 25, 30, . . . \}$

Which of the following are examples of the null set (ii) Set of even prime numbers

State whether each of the following statement is true or false. Justify your answer. (iv) \{ 2, 6, 10 \} and \{ 3, 7, 11\} are disjoint sets.

Find the intersection of each pair of sets of question 1 above.

Given the sets $A = \{1, 3, 5\}$, $B = \{2, 4, 6\}$ and $C = \{0, 2, 4, 6, 8\}$, which of the following may be considered as universal set (s) for all the three sets A, B and C

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (vi) If $A \subset B$ and $x \notin B$, then $x \notin A$

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (ii) If $A \subset B$ and $B \in C$, then $A \in C$

State whether each of the following statement is true or false. Justify your answer. (iii) \{ 2, 6, 10, 14 \} and \{ 3, 7, 11, 15\} are disjoint sets.

If $X= \{ a, b, c, d \}$ and $Y = \{ f, b, d, g\}$, find (iii) $X \cap Y$

Let $A = \{ a, b \}$, $B = \{a, b, c\}$. Is $A \subset B$ ? What is $A \cup B$ ?

Using properties of sets, show that (ii) $A \cap ( A \cup B ) = A$.

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 (iv) $B \cap C$

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces : (ii) \{ a, b, c \} . . . \{ b, c, d \}

Write the following sets in roster form: (i) $A = \{x : x$ is an integer and $–3 \le x < 7\}$

Taking the set of natural numbers as the universal set, write down the complements of the following sets: (x) $\{ x : x \ge 7 \}$

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