1) Prove or Disprove this claim 3(n, m) e Z × Z, [ 0 = (mm) mod 91 ] ^~[ (0 = n

Question

1) Prove or Disprove this claim 3(n, m) e Z × Z, [ 0 = (mm) mod 91 ] ^~[ (0 = n mod 91)s(0 = m mod 91)] English translation of the claim: There is at least one ordered pair of integers, (n, m), such that nm is an integer multiple of 91, but neither n nor m is an integer multiple of 91." 2) Prove or Disprove this claim: V n e Z, n2-19n + 101 is a prime number. English translation of the claim: For every integer n, the value of n2- 19n + 101 is a prime number." 3) Prove or Disprove this claim: (a, b) e2x Z, [ab is odd 1-1(a is odd) ^ (b is odd)] English translation of the claim: "For each ordered pair of integers, (a, b), if ab is odd, then both a and b are odd."

Explanation / Answer

1) true

n = 13, m= 7

as nm = 91 which is integral multiple of 91

but n and m are not

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