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SECTION 4. (b) The numerical analogue of the first of the relations in part (a) is (lim supx,)^(lim supy,) lim sup (x^y). n n PL Write out and verify the numerical analogues of the others. (c) Show that lim sup A,, - (lim inf A,), n n lim ini A (lim sup 4,)", A A n = lim sup A, - lim inf A, =lim sup (A,A+1) n n - lim sup (4%A, +1) A (d) Show that A, A and BB together imply that A, UB-AUB and AOBAO B.