Exercise - 1.1

. Write the following in roster form. (i) { x ∈ N : x < and x is a prime } . (ii) the set of all positive roots of the equation ( x − )( x + )( x − ) = .

(iii) { x ∈ N : x + < } . (iv) { x : x − x + = , x ∈ R −{− }} . . Write the set {− , } in set builder form.

. State whether the following sets are finite or infinite. (i) { x ∈ N : x is an even prime number } . (ii) { x ∈ N : x is an odd prime number } .

(iii) { x ∈ Z : x is even and less than } . (iv) { x ∈ R : x is a rational number } . (v) { x ∈ N : x is a rational number } . .

(v) ( B − A ) ∩ C = ( B ∩ C ) − A = B ∩ ( C − A ) . (vi) ( B − A ) ∪ C = ( B ∪ C ) − ( A − C ) . . Justify the trueness of the statement: “An element of a set can never be a subset of itself.” .

If n ( P ( A )) = , n ( A ∪ B ) = and n ( P ( B )) = , then find n ( A ∩ B ) . . If n ( A ∩ B ) = and n ( A ∪ B ) = , then find n ( P ( A ∆ B )) . .

For a set A, A × A contains elements and two of its elements are ( , ) and ( , ) . Find the elements of A.