Write the set of values of `n` for which the statement `P(n):2n < n!` is true.

Write the truth value of the statement: 2 ^(n) ge 2n for n in N

Write the truth values of the following statements: AA n in N, n2 + n is even number while n2- n is an odd number.

If P(n) is the statement n^(3)+n is divisible 3 is the statement P(3) true? Is the statement P(4) true?

If P(n) is the statement n^3+n is divisible 3 is the statement P(3) true ? Is the statement P(4) true?

Find whether the following statements are true or false. If the statement is false, then write its correct statement: (i) If P={m,n} and Q={n,m},then PxxQ={(m,n),(n,m)} . (ii) If A and B are non-empty sets, then AxxB is a non-empty set of the ordered pairs (x,y) such that x in A and y in B .

Find whether the following statements are true or false. If the statement is false, then write its correct statement: (i) If P={m,n} and Q={n,m},then PxxQ={(m,n),(n,m)} . (ii) If A and B are non-empty sets, then AxxB is a non-empty set of the ordered pairs (x,y) such that x in A and y in B .

If ZZ is the set of intergers and n in ZZ, then the value of n(n+1) (2n +1) -

A set contains (2n+1) elements.If the number of subsets of this set which contain atmost n elements is 4096, then n is