Give an example of a statement P(n) which is for all `n gt=4` but P(1) ,P(2) and P(3) are not true, justify your answer.

Give an example of a statement P(n) which is true for all n , justify your answer.

Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B ) ? Justify your answer.

Let P(n) denote the statement that n^2+n is odd . It is seen that P(n)rArr P(n+1),P(n) is true for all

Let P(n) be statement and let P(k) rArr P(k+1) ,for some natural number k, then P(n) is true for all n in N

If .^(n)P_(5)=20 .^(n)P_(3) , find the value of n.

Given a non empty set X , consider P(X) which is the set of all subsets of X. Define the relation R in P(X) as follows : For subsets A , B in P(X) ARB if and only if AsubB . Is R an equivalence relation on P(X) ? Justify your answer.

By giving a counter example, show that the following statements are not true. (i) p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.

For P(n):2^n = 0 ………..is true .