Use the method of direct proof to show that for any positive 5-digit integer n, if n is divisible by 9, then some of its digits is divisible by 9 too
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In each part, use the given method to prove/disprove the statements: Ka) Disprove the following statement by finding an appropriate counterexample: For every real numbers x, y, and z, if x > 0, y>0, and z>0, then 10-3z + x 2 + y 2 + z 2 s (x + y + z) (b) Use the method of exhaustion to prove the following statement: “For every prime number p between 30 and 58, 10 does not divide p-9." (c) Prove that 0.17461461 ... is rational (digits 461 in the fractional part are periodically repeated forever). (d) Use the method of direct proof to prove the following statement: Vm, n, 1 € Z,(m is even An is odd) + (ml + n is odd) (e) Use the method of direct proof to show that for any positive 5-digit integer n, if n is divisible by 9, then some of its digits is divisible by 9 too.