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    Bijections, Denumerability, Tautologies, Sets, Logic and Proofs (7 Problems)

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    Consider the compound statement (P ^ Q) V (~ P ^ R)

    a) Find the truth table for the statement.
    b) IS the statement a tautology?
    c) In the following program code, what has to be the output for the answr to be "yes"?
    ...
    2. Given the following sets A = {1.2,3.4}, B = {2,3,4,5}, and C= {2,4,6}
    a) Find ....

    4. Prove that if ... are bijections....then...is a bijection...

    5. Prove that the set of Gausian integers is denumerable.

    Please see the attached file for the fully formatted problems.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:19 pm ad1c9bdddf
    https://brainmass.com/math/discrete-math/bijections-denumerability-tautologies-sets-logic-proofs-40378

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    1. (a) 0-False, 1-True
    p q r p.q ~p.r p.q+~p.r
    0 0 0 0 0 0
    0 0 1 0 1 1
    0 1 0 0 0 0
    0 1 1 0 1 1
    1 0 0 0 0 0
    1 0 1 0 0 0
    1 1 0 1 0 1
    1 1 1 1 0 1

    (b) No. (p q) (~p r) is not Tautology as its value is not True always.

    (c) This block of program prints 'yes' when P is False and R is True

    2. A={1, 2, 3, 4}, B={2, 3, 4, 5} and C={2, 4, 6}

    A B={1, 2, 3, 4, 5}, A B={2, 3, 4}, ...

    Solution Summary

    Bijections, Denumerability, Tautologies, Sets, Logic and Proofs are investigated. The solution is detailed and well presented.

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