Show that `n{P{P(P(varphi))}}=4.`

Show that n[P[P.(P(phi)))=4

Show that n(P(P(P( phi))))=4

Show that (n+1)(""^(n)P_(r)) = (n-r+1)[""^(n+1)P_(r)]

Let P (n) denote the statement : “ 2^n gen ! ". Show that P(1), P(2) and P(3) are true but P(4) is not true.

Let P(n) denote the statement: 2^(n)ge n! .Show that P(1),P(2),P(3) are true butP(4) is not true.

Show that , .^(n)P_(r)=n.^(n-1)P_(r-1)=(n-r+1).^(n)P_(r-1) .

Show that P(m,1)+P (n,1)=P(M+n,1) for all positive integers m, n.

Show that (n +1) ("^(n)P_r) = (n - r + 1) ["^((n +1))P_r]

Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined as A" *"B" "=" "(A" "-" "B) uu(B" "-" "A), AA""""A ," "B in P(X) . Show that the empty set varphi is the identity for the operation * and all the elements A of P(A) are invertible with A^-1=A

Given a non -empty set X, let **: P(X) xx P(X) ->P(X) be defined as A **B = (A - B) uu(B - A), AAA , B in P(X) . Show that the empty set varphi is the identity for the operation ** and all the elements A of P(A) are invertible with A^-1 =A