Let the universe for both variables x and y be the set {2, 4, 6, 8, 10}. Let p(x,y) = "4 divides the sum x + y". Give the truth value of the indicated statement; explain your answer, and give a counterexample in case the statement is false.?y ?x p(x, y)
What will be an ideal response?
False.
For any y there is a counterexample:
choose y = 2, x = 4, 4 does not divide 6.
choose y = 4, x = 6, 4 does not divide 10.
choose y = 6, x =8, 4 does not divide 14.
choose y = 8, x = 10, 4 does not divide 18.
choose y = 10, x = 4, 4 does not divide 14.
Therefore, there does not exist a y, which for all x satisfies p(x).
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