State whether the following sets are finite or infinite.
{x \(\in \) N : x is an odd prime number}

State whether the following sets are finite or infinite.
{x \(\in \) Z : x is even and less than 10}

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1) (y, 2) (z, 1) are in A\(\times\)B, find A and B, where x, y, z are distinct elements.

Let X = {a, b, c, d}, and R = {(a, a) (b, b) (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it 
(i) reflexive
(ii) symmetric
(iii) transitive
(iv) equivalence

If U = {x : 1 ≤ x ≤ 10, x ∈ N}, A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 9, 10} then find A'UB'.

If A⊂B then find A⋂B and A\B (using venn diagram)

On the set of natural number let R be the relation defined by aRb if a + b \(\le\) 6. Write down the relation by listing all the pairs. Check whether it is reflexive

On the set of natural number let R be the relation defined by aRb if a + b \(\le\) 6. Write down the relation by listing all the pairs. Check whether it is symmetric

Find the number of subsets of A if A = \(\{x :x = 4n + 1, 2 \le n \le 5, n \in N\}.\)

If f and g are two functions from R to R defined by f (x) = 4x - 3, g(x) = x² + 1, find fog and gof.

On a set of natural numbers let R be the relation defined by aRb if a + 2b = 15. Write down the relation by listing all the pairs. Check whether it is reflexive, symmetric, transitive, equivalence.

If  \(f(x)=\frac { x-1 }{ x+1 } \), then show that \(f\left( \frac { 1 }{ x } \right) =-f(x)\)

If  f(x) = \(\frac { x-1 }{ x+1 } \), then show that, f\(\left( \frac { -1 }{ x } \right) =\frac { -1 }{ f(x) } \).

If A = { 0, 1, 2, 3, 4, 5, 6, 7 } is a set. Then,

Try to write the following intervals in symbolic form:
(i) \(\{x:x\in R,-2\le x \le 0 \},\) 
(ii) \(\{ x:x\in R, 0\)
(iii) \(\{ x:x \in R, -8\le -2 \}\)
(iv) \(\{x:x\in R, -5\le x \le 9 \}\)