contraposition

  1. T

    proof by contraposition help

    m is an integer. Prove by contraposition that if 5m + 4 is odd then m is odd suppose m is even, than m = 2n for some n in N so 5(2n) +4 = 20n+4 factor out 2 = 2(10n+2) which is even, have i proved this ? ]
  2. S

    prove by contradiction and contraposition, (a | b and ~( a | c) ) --> ~( a | b+c)

    For some reason I'm stuck on this. For proof by contraposition: For all integers a,b,c a | b+c --> ~(a | b) or (a | c). Suppose a | b+c b+c=a*k for some integer k ... I can't figure out exactly where to go from here. By contradiction: suppose there exists integers a,b,c such that a |...
  3. mremwo

    Proof by Contraposition... (and background hypothesis PLEASE HELP!)

    Prove by using proof by contraposition (and background hypothesis) that "the product of a non-zero rational number m and irrational number n is irrational.... im supposed to use contraposition and background hypothesis to change this statement to... in the background ---> (m not equal to 0)...
  4. D

    Need help proving by contraposition

    Hello, I have a home work question that asks me to prove by contraposition that for all positive real numbers that if x is irrational, then x^1/2 is also irrational. So far I have the Contrapositive of for all positive real numbers, x^1/2 is rational then x is rational. Which means...
  5. D

    direct proof or contraposition?

    I am asked to proof this conjecture: If x is rational and x is not equal to 0, then 1/x is rational. How do I proof this? Should I use direct or contraposition proof? I just learned about this stuff and I don't know where to start at.